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 A117903 #11 Sep 08 2022 08:45:24
%S A117903 1,-1,1,-2,4,-2,-5,14,-5,-26,64,-26,-101,254,-101,-410,1024,-410,
%T A117903 -1637,4094,-1637,-6554,16384,-6554,-26213,65534,-26213,-104858,
%U A117903 262144,-104858,-419429
%N A117903 Diagonal sums of number triangle A117901.
%H A117903 Harvey P. Dale, <a href="/A117903/b117903.txt">Table of n, a(n) for n = 0..1000</a>
%H A117903 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,3,3,3,4,4,4).
%F A117903 G.f.: (1+x^2-5*x^3+3*x^4-3*x^5-x^6-2*x^7)/((1-4*x^3)*(1+x+x^2+x^3+x^4+x^5)).
%F A117903 a(n) = -a(n-1) -a(n-2) +3*a(n-3) +3*a(n-4) +3*a(n-5) +4*a(n-6) +4*a(n-7) +4*a(n-8).
%F A117903 a(n) = (1/30)*(28*(-1)^n + (15*(-1)^n - 1)*A057079(n) - 6*(2*A133851(n) - 5*A133851(n-1) + 2*A133851(n-2))). - _G. C. Greubel_, Oct 09 2021
%t A117903 LinearRecurrence[{-1,-1,3,3,3,4,4,4},{1,-1,1,-2,4,-2,-5,14},40] (* _Harvey P. Dale_, Oct 04 2021 *)
%o A117903 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^2-5*x^3+3*x^4-3*x^5-x^6-2*x^7)/((1-4*x^3)*(1+x+x^2+x^3+x^4+x^5)) )); // _G. C. Greubel_, Oct 09 2021
%o A117903 (Sage)
%o A117903 def A133851(n): return 4^(n/3) if (n%3==0) else 0
%o A117903 def A057079(n): return chebyshev_U(n, 1/2) + chebyshev_U(n-1, 1/2)
%o A117903 def A117903(n): return (1/30)*(28*(-1)^n + (15*(-1)^n - 1)* A057079(n) - 6*(2*A133851(n) - 5*A133851(n-1) + 2*A133851(n-2)))
%o A117903 [A117903(n) for n in (0..50)] # _G. C. Greubel_, Oct 09 2021
%Y A117903 Cf. A057079, A117901, A133851.
%K A117903 easy,sign
%O A117903 0,4
%A A117903 _Paul Barry_, Apr 01 2006