cp's OEIS Frontend

A104969 Sum of squares of terms in rows of triangle A104967.

%I A104969 #7 Jun 09 2021 22:38:35
%S A104969 1,2,6,12,18,36,92,184,298,596,1444,2888,4852,9704,22840,45680,78490,
%T A104969 156980,362580,725160,1265564,2531128,5767688,11535376,20366596,
%U A104969 40733192,91866984,183733968,327351336,654702672,1464522864,2929045728
%N A104969 Sum of squares of terms in rows of triangle A104967.
%H A104969 G. C. Greubel, <a href="/A104969/b104969.txt">Table of n, a(n) for n = 0..500</a>
%F A104969 a(2*n+1) = 2*a(2*n).
%F A104969 G.f.: A(x) = (1+2*x)*G(x^2) where G(x) is the g.f. of A104970 such that G(x) satisfies: 2*(1+12*x)*G(x) - (1-16*x^2)*deriv(G(x), x) + 4 = 0.
%F A104969 a(n) = Sum_{k=0..n} (A104967(n, k))^2.
%t A104969 A104967[n_, k_]:= A104967[n, k]= Sum[(-2)^j*Binomial[k+1, j]*Binomial[n-j, k], {j, 0, n-k}];
%t A104969 A104969[n_]:= A104969[n]= Sum[A104967[n, k]^2, {k,0,n}];
%t A104969 Table[A104969[n], {n, 0, 50}] (* _G. C. Greubel_, Jun 09 2021 *)
%o A104969 (PARI) {a(n)=local(X=x+x*O(x^n)); sum(k=0,n,polcoeff(polcoeff((1-2*X)/(1-X-X*y*(1-2*X)),n,x),k,y)^2)}
%o A104969 (Sage)
%o A104969 @cached_function
%o A104969 def A104967(n,k): return sum( (-2)^j*binomial(k+1,j)*binomial(n-j,k) for j in (0..n-k))
%o A104969 def A104969(n): return sum((A104967(n,k))^2 for k in (0..n))
%o A104969 [A104969(n) for n in (0..50)] # _G. C. Greubel_, Jun 09 2021
%Y A104969 Cf. A104967, A104968, A104970.
%K A104969 nonn
%O A104969 0,2
%A A104969 _Paul D. Hanna_, Mar 30 2005