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A129366 a(n)=sum{k=0..floor(n/2), C(n-k)}, C(n)=A000108(n). 1
1, 1, 3, 7, 21, 61, 193, 617, 2047, 6895, 23691, 82435, 290447, 1033215, 3707655, 13402071, 48759741, 178403101, 656041801, 2423300129, 8987420549, 33453670773, 124936234413, 467995789277, 1757899936601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of (A129367 prefixed by an initial 1).

LINKS

Table of n, a(n) for n=0..24.

FORMULA

G.f.: (1/(1-x))(c(x)-xc(x^2)), c(x) the g.f. of A000108(n); G.f.: (sqrt(1-4x^2)-sqrt(1-4x))/(2x(1-x)); a(n)=sum{k=floor((n+1)/2)..n, C(k)};

Conjecture: +n*(12*n+35)*(n-1)*a(n) +(n-1)*(12*n^2-701*n+1236)*a(n-1) +2*(6*n^3-385*n^2+2285*n-3432)*a(n-2) +4*(-405*n^3+5313*n^2-19970*n+23175)*a(n-3) +8*(156*n^3-1724*n^2+5498*n-5175)*a(n-4) +16*(393*n^3-4981*n^2+20393*n-26820)*a(n-5) -32*(n-5)*(93*n-268)*(2*n-9)*a(n-6)=0. - R. J. Mathar, Feb 05 2015

CROSSREFS

Sequence in context: A005355 A182399 A025235 * A270049 A166358 A148670

Adjacent sequences:  A129363 A129364 A129365 * A129367 A129368 A129369

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 11 2007

STATUS

approved

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Last modified July 20 16:15 EDT 2019. Contains 325185 sequences. (Running on oeis4.)