A056119 a(n) = n*(n+13)/2.
0, 7, 15, 24, 34, 45, 57, 70, 84, 99, 115, 132, 150, 169, 189, 210, 232, 255, 279, 304, 330, 357, 385, 414, 444, 475, 507, 540, 574, 609, 645, 682, 720, 759, 799, 840, 882, 925, 969, 1014, 1060, 1107, 1155, 1204, 1254, 1305, 1357, 1410, 1464, 1519, 1575
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- P. Lafer, Discovering the square-triangular numbers, Fib. Quart., 9 (1971), 93-105.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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GAP
List([0..50], n-> n*(n+13)/2 ); # G. C. Greubel, Jan 18 2020
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Magma
[n*(n+13)/2: n in [0..50]]; // G. C. Greubel, Jan 18 2020
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Mathematica
Table[n*(n+13)/2, {n, 0, 50}] (* Paolo Xausa, Jun 26 2024 *) -
PARI
a(n)=n*(n+13)/2 \\ Charles R Greathouse IV, Oct 07 2015
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Sage
[n*(n+13)/2 for n in (0..50)] # G. C. Greubel, Jan 18 2020
Formula
G.f.: x*(7-6*x)/(1-x)^3.
a(n) = A126890(n,6) for n > 5. - Reinhard Zumkeller, Dec 30 2006
a(n) = A000096(n) + 5*A001477(n) = A056115(n) + A001477(n) = A056121(n) - A001477(n). - Zerinvary Lajos, Feb 22 2008
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,7), for n >= 1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 6 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
Sum_{n>=1} 1/a(n) = 1145993/2342340 via A132759. - R. J. Mathar, Jul 14 2012
a(n) = 7*n - floor(n/2) + floor(n/2). - Wesley Ivan Hurt, Jun 15 2013
E.g.f.: x*(14 + x)*exp(x)/2. - G. C. Greubel, Jan 18 2020
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/13 - 263111/2342340. - Amiram Eldar, Jan 10 2021
Extensions
More terms from James Sellers, Jul 05 2000