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A086905 a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(k,floor(k/2)). 3
1, 0, 2, 1, 5, 5, 15, 20, 50, 76, 176, 286, 638, 1078, 2354, 4081, 8789, 15521, 33099, 59279, 125477, 227239, 478193, 873885, 1830271, 3370029, 7030571, 13027729, 27088871, 50469889, 104647631, 195892564, 405187826, 761615284, 1571990936 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Knödel walks starting and ending at 0, with n steps.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

H. Prodinger, The Kernel Method: a collection of examples, Séminaire Lotharingien de Combinatoire, B50f (2004), 19 pp.

FORMULA

G.f.: (sqrt((1+2*x)/(1-2*x))-1)/2/x/(1+x).

a(n) ~ 2^(n+3/2) / (3*sqrt(Pi*n)) * (1 - 2/(3*n)+ 3*(-1)^n/(4*n)). - Vaclav Kotesovec, Mar 02 2014

MATHEMATICA

Table[Sum[(-1)^(n-k)*Binomial[k, Floor[k/2]], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *)

PROG

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k, k\2)); \\ Michel Marcus, Dec 04 2016

CROSSREFS

Cf. A036256, A001405.

First column of triangle A101491.

Sequence in context: A119245 A128731 A129157 * A167638 A209108 A269019

Adjacent sequences:  A086902 A086903 A086904 * A086906 A086907 A086908

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Sep 19 2003

STATUS

approved

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Last modified February 21 16:41 EST 2018. Contains 299414 sequences. (Running on oeis4.)