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A104969
Sum of squares of terms in rows of triangle A104967.
5
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
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 30 2005
STATUS
approved