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 A110198 #22 Mar 21 2025 09:35:35
%S A110198 1,2,4,9,20,46,109,262,638,1569,3886,9680,24225,60856,153368,387573,
%T A110198 981742,2491934,6336721,16139616,41166912,105139773,268841100,
%U A110198 688157430,1763206441,4521749642,11605580290,29809644693,76621733444,197074591420,507193044993
%N A110198 Antidiagonal sums of number triangle A110197.
%C A110198 Partial sums of A051286.
%H A110198 Vincenzo Librandi, <a href="/A110198/b110198.txt">Table of n, a(n) for n = 0..1000</a>
%F A110198 G.f.: 1/((1-x)*sqrt((1+x+x^2)*(1-3x+x^2))); a(n) = sum{k=0..floor(n/2), sum{i=0..n-2k, binomial(i+k, k)^2}}.
%F A110198 a(n) = sum{i=0..2n, A202411(i)}. - _Peter Luschny_, Jan 16 2012
%F A110198 Conjecture: n*a(n) +(-3*n+1)*a(n-1) +n*a(n-2) +(-n+2)*a(n-3) +(3*n-5)*a(n-4) +(-n+2)*a(n-5)=0. - _R. J. Mathar_, Nov 15 2012
%F A110198 a(n) ~ sqrt(100+45*sqrt(5)) * ((sqrt(5)+3)/2)^n / (10*sqrt(Pi*n)). - _Vaclav Kotesovec_, Feb 08 2014
%F A110198 Equivalently, a(n) ~ phi^(2*n + 3) / (2 * 5^(1/4) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - _Vaclav Kotesovec_, Dec 07 2021
%t A110198 CoefficientList[Series[1/((1-x)*Sqrt[(1+x+x^2)*(1-3*x+x^2)]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 08 2014 *)
%Y A110198 Cf. A051286, A110197, A201631.
%K A110198 easy,nonn
%O A110198 0,2
%A A110198 _Paul Barry_, Jul 15 2005