A176750 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)=4, k=0 and l=-1.

1, 4, 7, 29, 113, 506, 2321, 11112, 54429, 272364, 1384701, 7135397, 37178543, 195556526, 1036967927, 5537451445, 29752654081, 160731437308, 872518135861, 4756932856431, 26035840213731, 143003903810742, 787983925181427

Offset

0,2

Links

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

Formula

G.f 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=0, l=-1).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-3*n+11)*a(n-2) +4*(6*n-19)*a(n-3) +16*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016

Example

a(2)=2*1*4-1=7. a(3)=2*1*7+4^2-1=29. a(4)=2*1*29+2*4*7-1=113.

Maple

l:=-1: : k := 0 : m:=4: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. A176749.

Sequence in context: A272870 A377458 A362650 * A030687 A149081 A149082

Adjacent sequences: A176747 A176748 A176749 * A176751 A176752 A176753

Keyword

easy,nonn

Author

Richard Choulet, Apr 25 2010

Status

approved