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 A115217 #19 Aug 30 2025 12:36:12
%S A115217 1,2,6,13,30,62,133,270,558,1125,2286,4590,9253,18542,37230,74533,
%T A115217 149358,298862,598309,1196910,2394990,4790565,9583470,19168110,
%U A115217 38340901,76684142,153377646,306759973,613538670,1227086702,2454210853
%N A115217 Diagonal sums of "correlation triangle" for 2^n.
%C A115217 Diagonal sums of number triangle A003983.
%H A115217 Harvey P. Dale, <a href="/A115217/b115217.txt">Table of n, a(n) for n = 0..1000</a>
%H A115217 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-3,-2,-2,4).
%F A115217 a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..n-k} [j<=k]*2^(k-j)*[j<=n-2k]*2^(n-2k-j).
%F A115217 From _Paul Barry_, Jan 18 2006: (Start)
%F A115217 G.f.: 1/((1-2*x)*(1-2*x^2)*(1-x^3)).
%F A115217 a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3) - 2*a(n-4) - 2*a(n-5) + 4*a(n-6). (End)
%F A115217 E.g.f.: (exp(x)*(7 + 48*exp(x)) + 2*exp(-x/2)*cos(sqrt(3)*x/2) - 36*cosh(sqrt(2)*x) - 30*sqrt(2)*sinh(sqrt(2)*x))/21. - _Stefano Spezia_, Aug 28 2025
%t A115217 LinearRecurrence[{2,2,-3,-2,-2,4},{1,2,6,13,30,62},40] (* _Harvey P. Dale_, Oct 18 2021 *)
%Y A115217 Cf. A003983.
%K A115217 easy,nonn,changed
%O A115217 0,2
%A A115217 _Paul Barry_, Jan 16 2006