This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A056119 #62 Jul 02 2025 16:02:00
%S A056119 0,7,15,24,34,45,57,70,84,99,115,132,150,169,189,210,232,255,279,304,
%T A056119 330,357,385,414,444,475,507,540,574,609,645,682,720,759,799,840,882,
%U A056119 925,969,1014,1060,1107,1155,1204,1254,1305,1357,1410,1464,1519,1575
%N A056119 a(n) = n*(n+13)/2.
%H A056119 G. C. Greubel, <a href="/A056119/b056119.txt">Table of n, a(n) for n = 0..1000</a>
%H A056119 P. Lafer, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/9-1/lafer.pdf">Discovering the square-triangular numbers</a>, Fib. Quart., 9 (1971), 93-105.
%H A056119 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A056119 G.f.: x*(7-6*x)/(1-x)^3.
%F A056119 a(n) = A126890(n,6) for n > 5. - _Reinhard Zumkeller_, Dec 30 2006
%F A056119 a(n) = A000096(n) + 5*A001477(n) = A056115(n) + A001477(n) = A056121(n) - A001477(n). - _Zerinvary Lajos_, Feb 22 2008
%F A056119 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
%F A056119 a(n) = n + a(n-1) + 6 (with a(0)=0). - _Vincenzo Librandi_, Aug 07 2010
%F A056119 Sum_{n>=1} 1/a(n) = 1145993/2342340 via A132759. - _R. J. Mathar_, Jul 14 2012
%F A056119 a(n) = 7*n - floor(n/2) + floor(n/2). - _Wesley Ivan Hurt_, Jun 15 2013
%F A056119 E.g.f.: x*(14 + x)*exp(x)/2. - _G. C. Greubel_, Jan 18 2020
%F A056119 Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/13 - 263111/2342340. - _Amiram Eldar_, Jan 10 2021
%t A056119 Table[n*(n+13)/2, {n, 0, 50}] (* _Paolo Xausa_, Jun 26 2024 *)
%o A056119 (PARI) a(n)=n*(n+13)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A056119 (Magma) [n*(n+13)/2: n in [0..50]]; // _G. C. Greubel_, Jan 18 2020
%o A056119 (Sage) [n*(n+13)/2 for n in (0..50)] # _G. C. Greubel_, Jan 18 2020
%o A056119 (GAP) List([0..50], n-> n*(n+13)/2 ); # _G. C. Greubel_, Jan 18 2020
%Y A056119 Cf. A000096, A001477, A056000, A056115, A056121.
%K A056119 easy,nonn
%O A056119 0,2
%A A056119 _Barry E. Williams_, Jul 04 2000
%E A056119 More terms from _James Sellers_, Jul 05 2000