A176829 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=3, k=1 and l=-1.

1, 3, 7, 25, 95, 393, 1711, 7741, 36007, 171097, 826839, 4050957, 20074303, 100438233, 506677279, 2574292749, 13161031191, 67656253081, 349499197799, 1813347470669, 9445448148975, 49375113712089, 258938850241327

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: f(z) = (1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=1, l=-1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(7*n-5)*a(n-2) +(7*n-26)*a(n-3) +4*(-4*n+17)*a(n-4) +8*(n-5)*a(n-5)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*3+2-1=7. a(3)=2*1*7+2+3^2+1-1=25. a(4)=2*1*25+2+2*3*7+2-1=95.

Maple

l:=-1: : k := 1 : m:=3:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od : taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);

Crossrefs

Cf. A176828.

Sequence in context: A096579 A350650 A120540 * A352385 A133206 A054092

Adjacent sequences: A176826 A176827 A176828 * A176830 A176831 A176832

Keyword

easy,nonn

Author

Richard Choulet, Apr 27 2010

Status

approved