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

1, 2, 6, 12, 18, 36, 92, 184, 298, 596, 1444, 2888, 4852, 9704, 22840, 45680, 78490, 156980, 362580, 725160, 1265564, 2531128, 5767688, 11535376, 20366596, 40733192, 91866984, 183733968, 327351336, 654702672, 1464522864, 2929045728

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

a(2*n+1) = 2*a(2*n).

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.

a(n) = Sum_{k=0..n} (A104967(n, k))^2.

Mathematica

A104967[n_, k_]:= A104967[n, k]= Sum[(-2)^j*Binomial[k+1, j]*Binomial[n-j, k], {j, 0, n-k}];
A104969[n_]:= A104969[n]= Sum[A104967[n, k]^2, {k, 0, n}];
Table[A104969[n], {n, 0, 50}] (* G. C. Greubel, Jun 09 2021 *)

Prog

(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)}
(Sage)
@cached_function
def A104967(n, k): return sum( (-2)^j*binomial(k+1, j)*binomial(n-j, k) for j in (0..n-k))
def A104969(n): return sum((A104967(n, k))^2 for k in (0..n))
[A104969(n) for n in (0..50)] # G. C. Greubel, Jun 09 2021

Crossrefs

Cf. A104967, A104968, A104970.

Sequence in context: A125024 A178480 A053660 * A065005 A299016 A347472

Adjacent sequences: A104966 A104967 A104968 * A104970 A104971 A104972

Keyword

nonn

Author

Paul D. Hanna, Mar 30 2005

Status

approved