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A117186 Expansion of (1+x)c(x^2)/((1-xc(x^2))*sqrt(1-4x^2)), c(x) the g.f. of A000108. 2
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 (list; graph; refs; listen; history; text; internal format)
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). [From 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: A105309 A192572 A097163 * A155042 A001851 A024822

Adjacent sequences:  A117183 A117184 A117185 * A117187 A117188 A117189

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 01 2006

STATUS

approved

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Last modified November 21 16:27 EST 2017. Contains 295003 sequences.