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 A079810 #12 Dec 13 2023 08:32:14
%S A079810 1,1,5,3,8,8,16,12,21,21,33,27,40,40,56,48,65,65,85,75,96,96,120,108,
%T A079810 133,133,161,147,176,176,208,192,225,225,261,243,280,280,320,300,341,
%U A079810 341,385,363,408,408,456,432,481,481,533,507,560,560,616,588,645,645
%N A079810 Sums of diagonals (upward from left to right) of the triangle shown in A079809.
%H A079810 G. C. Greubel, <a href="/A079810/b079810.txt">Table of n, a(n) for n = 1..1000</a>
%H A079810 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,2,-2,0,0,-1,1).
%F A079810 a(4k) = 3k^2. a(4k+1) = a(4k+2) = 3k^2+4k+1. a(4k+3) = 3k^2+8k+5.
%F A079810 From _Chai Wah Wu_, Feb 03 2021: (Start)
%F A079810 a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) - a(n-8) + a(n-9) for n > 9.
%F A079810 G.f.: x*(1 + 4*x^2 - 2*x^3 + 3*x^4)/((1 - x)^3*(1 + x)^2*(1 + x^2)^2). (End)
%F A079810 From _G. C. Greubel_, Dec 12 2023: (Start)
%F A079810 a(n) = (1/32)*( (6*n^2 + 14*n + 5) - (-1)^n*(10*n + 9) + 2*((3 - i)*(-i)^n + (3 + i)*i^n) - 8*(-1)^floor(n/2)*floor((n+2)/2) ).
%F A079810 E.g.f.: 4*(1-x)*cos(x) - 4*(2-x)*sin(x) + 2*(3*x^2 + 15*x - 2)*cosh(x) 2*(3*x^2 + 5*x + 7)*sinh(x). (End)
%e A079810 a(7) = T(7,1) + T(6,2) + T(5,3) + T(4,4) = 7 + 2 + 3 + 4 = 16.
%t A079810 LinearRecurrence[{1,0,0,2,-2,0,0,-1,1}, {1,1,5,3,8,8,16,12,21}, 70] (* _G. C. Greubel_, Dec 12 2023 *)
%o A079810 (Magma) R<x>:=PowerSeriesRing(Integers(), 71); Coefficients(R!( x*(1+4*x^2-2*x^3+3*x^4)/((1-x)*(1-x^4)^2) )); // _G. C. Greubel_, Dec 12 2023
%o A079810 (SageMath)
%o A079810 def A079810_list(prec):
%o A079810 P.<x> = PowerSeriesRing(ZZ, prec)
%o A079810 return P( x*(1+4*x^2-2*x^3+3*x^4)/((1-x)*(1-x^4)^2) ).list()
%o A079810 a=A079810_list(71); a[1:] # _G. C. Greubel_, Dec 12 2023
%Y A079810 Cf. A079808, A079809, A079811, A092542.
%K A079810 nonn
%O A079810 1,3
%A A079810 _Amarnath Murthy_, Feb 10 2003
%E A079810 Edited by _David Wasserman_, May 11 2004