A247173 Expansion of g.f. (-1)/(2*x^2+2*x) +(-2*x^3-3*x^2+1) / (sqrt(x^4+4*x^3-2*x^2-4*x+1)*(2*x^2+2*x)).

1, 1, 7, 25, 101, 397, 1583, 6337, 25513, 103161, 418727, 1705129, 6963165, 28504981, 116941727, 480667137, 1979039633, 8160609457, 33696358983, 139308985465, 576583448021, 2388853677981, 9906585874127, 41118073118785, 170799570803001, 710003165365417

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = (n+1)*sum(k=0..n, (C(n-k-1,k)*sum(i=0..n-k, 2^i*C(k+1,n-k-i) *C(k+i,k)*(-1)^(n-k-i)))/(k+1)).

Conjecture D-finite with recurrence: -(n+1)*(3*n-4)*a(n) +(9*n^2-3*n-4)*a(n-1) +2*(9*n^2-21*n+8)*a(n-2) +2*(-3*n^2+n+8)*a(n-3) +(-15*n^2+53*n-12)*a(n-4) -(3*n-1)*(n-4)*a(n-5)=0. - R. J. Mathar, Jan 25 2020

a(n) ~ 5^(1/4) * phi^(3*n + 2) / (2^(3/2) * sqrt(Pi*n)), where phi = A001622 is the golden ratio. - Vaclav Kotesovec, Nov 19 2021

Prog

(Maxima) a(n):=(n+1)*sum((binomial(n-k-1, k)*sum(2^i*binomial(k+1, n-k-i)*binomial(k+i, k)*(-1)^(n-k-i), i, 0, n-k))/(k+1), k, 0, n);

Crossrefs

Sequence in context: A138729 A035509 A332942 * A141627 A289606 A102900

Adjacent sequences: A247170 A247171 A247172 * A247174 A247175 A247176

Keyword

nonn

Author

Vladimir Kruchinin, Nov 22 2014

Status

approved