A117186 Expansion of (1+x)c(x^2)/((1-xc(x^2))*sqrt(1-4x^2)), c(x) the g.f. of A000108.

1, 2, 5, 9, 21, 38, 86, 157, 349, 642, 1410, 2610, 5682, 10572, 22860, 42717, 91869, 172298, 368906, 694054, 1480486, 2793012, 5938740, 11230834, 23813746, 45131348, 95462996, 181268292, 382594884, 727747608, 1533053976

Offset

0,2

Comments

Row sums of triangle A117184.

Links

Table of n, a(n) for n=0..30.

Formula

G.f.: (1+x)(sqrt(1-4x^2)+2x-1)/(2x(1-2x)*sqrt(1-4x^2)); a(n)=sum{k=0..n, C(n+1,(n+k)/2+1)(1+(-1)^(n-k))/2+C(n,(n+k)/2+1/2)(1-(-1)^(n-k))/2}.

G.f.: (1+x)(1+2x-sqrt(1-4x^2))/(2x(1-4x^2)); a(n)=(3*2^n-binomial(2*floor((n+1)/2),floor((n+1)/2)))/2; - Paul Barry, Jan 20 2008

Conjecture: a(n) = A058622(n) + A058622(n+1). [R. J. Mathar, Nov 21 2008]

Conjecture: -(n+1)*a(n) +(n+1)*a(n-1) +2*(3*n-2)*a(n-2) -4*n*a(n-3) +8*(3-n)*a(n-4)=0. - R. J. Mathar, Nov 15 2011

Crossrefs

Sequence in context: A192572 A300531 A097163 * A155042 A001851 A356375

Adjacent sequences: A117183 A117184 A117185 * A117187 A117188 A117189

Keyword

easy,nonn

Author

Paul Barry, Mar 01 2006

Status

approved