OFFSET
0,2
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (4,0,-8,-4).
FORMULA
a(n) = Sum_{k=0..n} b(k)*b(n-k), with b(k) = A002605(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+1, 1)*binomial(n-k, k)*2^(n-k).
a(n) = ((n+1)*U(n+1) + 2*(n+2)*U(n))/6, with U(n) = A002605(n), n >= 0.
G.f.: 1/(1-2*x*(1+x))^2.
a(n) = Sum_{k=0..floor((n+2)/2)} k*binomial(n-k+2, k)2^(n-k+1). - Paul Barry, Oct 15 2004
MATHEMATICA
CoefficientList[Series[1/(1-2*x-2*x^2)^2, {x, 0, 40}], x] (* G. C. Greubel, Oct 03 2022 *)
PROG
(Sage) taylor( 1/(1-2*x-2*x^2)^2, x, 0, 24).list() # Zerinvary Lajos, Jun 03 2009; modified by G. C. Greubel, Oct 03 2022
(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+1, 1)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^2 )); // G. C. Greubel, Oct 03 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 02 2002
STATUS
approved