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A176956 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
1, 3, 3, 11, 35, 139, 547, 2251, 9379, 39819, 171171, 744651, 3271203, 14494859, 64707875, 290773707, 1314227619, 5970720651, 27251241891, 124895810251, 574563563299, 2652205841547, 12280754200611, 57026615362763 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

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=-1, l=-1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(7*n-5)*a(n-2) +(23*n-82)*a(n-3) +4*(-10*n+41)*a(n-4) +16*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

EXAMPLE

a(2)=2*1*3-2-1=3. a(3)=2*1*3-2+9-1-1=11. a(4)=2*1*11+2*3*3-2-2-1=35.

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. A176954.

Sequence in context: A163938 A109937 A054101 * A200861 A113892 A334283

Adjacent sequences:  A176953 A176954 A176955 * A176957 A176958 A176959

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 29 2010

STATUS

approved

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Last modified April 17 05:12 EDT 2021. Contains 343059 sequences. (Running on oeis4.)