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A051942
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a(n) = n*(n+1)/2 - 45.
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12
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0, 10, 21, 33, 46, 60, 75, 91, 108, 126, 145, 165, 186, 208, 231, 255, 280, 306, 333, 361, 390, 420, 451, 483, 516, 550, 585, 621, 658, 696, 735, 775, 816, 858, 901, 945, 990, 1036, 1083, 1131, 1180, 1230, 1281, 1333, 1386, 1440, 1495, 1551, 1608, 1666
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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9,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 9..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = (n^2 + n - 90)/2 = (n-9)*(n+10)/2 = n*(n+1)/2 - 45.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n>=13.
a(n) = n + a(n-1) (with a(9) = 0). - Vincenzo Librandi, Aug 06 2010
G.f.: x^10*(10 - 9*x)/(1-x)^3.
From Amiram Eldar, Jan 10 2021: (Start)
Sum_{n>=10} 1/a(n) = 2*A001008(19)/(19*A002805(19)) = 275295799/737176440.
Sum_{n>=10} (-1)^n/a(n) = 4*log(2)/19 - 33464927/442305864. (End)
E.g.f.: (1/8!)*(1814400 +1774080*x +846720*x^2 +262080*x^3 +58800*x^4 +10080*x^5 +1344*x^6 +136*x^7 +9*x^8 - (1814400 -40320*x -20160*x^2)*exp(x)). - G. C. Greubel, Jul 31 2022
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EXAMPLE
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a(10) = 10 + 0 = 10;
a(11) = 11 + 10 = 21;
a(12) = 12 + 21 = 33.
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MAPLE
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A051942:=n->(n^2+n-90)/2: seq(A051942(n), n=9..80); # Wesley Ivan Hurt, Jan 28 2017
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MATHEMATICA
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Table[n(n+1)/2 -45, {n, 9, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)
#-45&/@Drop[Accumulate[Range[60]], 8] (* Harvey P. Dale, Jul 24 2011 *)
LinearRecurrence[{3, -3, 1}, {0, 10, 21}, 60] (* Harvey P. Dale, Mar 25 2015 *)
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PROG
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(PARI) a(n)=(n-9)*(n+10)/2;
(Magma) [(n-9)*(n+10)/2: n in [9..80]]; // G. C. Greubel, Jul 31 2022
(SageMath) [(n-9)*(n+10)/2 for n in (9..80)] # G. C. Greubel, Jul 31 2022
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CROSSREFS
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Cf. A000096, A001008, A001477, A002805, A056121, A056126, A079664.
Sequence in context: A184989 A072806 A189402 * A250664 A082581 A075846
Adjacent sequences: A051939 A051940 A051941 * A051943 A051944 A051945
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KEYWORD
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easy,nice,nonn
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 21 1999
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EXTENSIONS
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More terms from Zerinvary Lajos, Oct 01 2006
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STATUS
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approved
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