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A335087 Row sums of A335436.

%I A335087 #29 Sep 14 2020 00:33:44
%S A335087 1,7,34,150,628,2540,10024,38840,148368,560368,2096928,7786592,
%T A335087 28726592,105390272,384788096,1398978432,5067403520,18294707968,
%U A335087 65854095872,236421150208,846732997632,3025927678976,10792083499008,38420157773824,136547503083520,484546494459904,1716976084393984
%N A335087 Row sums of A335436.
%C A335087 This sequence is also a composition of generating functions H(x) = G(F(x)), where G(x) = x/(1-4*x)^2 is the generating function of A002697 and F(x) = x*(1-x)/(1-2*x^2) is the generating function of 0, A016116*(-1)^n.
%H A335087 Oboifeng Dira, <a href="http://www.seams-bull-math.ynu.edu.cn/downloadfile.jsp?filemenu=_201706&amp;filename=07_41(6).pdf">A Note on Composition and Recursion</a>, Southeast Asian Bulletin of Mathematics (2017), Vol. 41, Issue 6, 849-853.
%H A335087 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (8,-20,16,-4).
%F A335087 a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-4*a(n-4), a(0)=1, a(1)=7, a(2)=34, a(3)=150 for  n>=4.
%F A335087 G.f.: (1-x)*(1-2*x^2)/(1-4*x+2*x^2)^2.
%F A335087 a(0)=1; a(n) = 2*n+1+Sum_{k=1..n}[(2+sqrt(2))^(k+1)-(2-sqrt(2))^(k+1)]*(2n-k+1)/(4*sqrt(2)), n>=1.
%F A335087 G.f.: G(F(x))/x where G(x) is g.f of A002697 and F(x) is g.f of 0,A016116*(-1)^n.
%e A335087 For n = 4, a(4) = 8*a(3)-20*a(2)+16*a(1)-4*a(0) = 8*150-20*34+16*7-4*1 = 628.
%p A335087 f:=x->x*(1-x)/(1-2*x^2):g:=x->(x)/(1-4*x)^2:
%p A335087 C:=n->coeff(series(g(f(x))/x,x,n+1),x,n): seq(C(n),n=0..30);
%Y A335087 Composition of g.fs of A002697 and A016116.
%Y A335087 Cf. A335436.
%K A335087 nonn
%O A335087 0,2
%A A335087 _Oboifeng Dira_, Sep 11 2020