A383577 - OEIS

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A383577

a(n) = Sum_{k=0..floor(n/3)} binomial(n-k,k) * binomial(n-2*k,k)^2.

0

1, 1, 1, 3, 13, 37, 87, 241, 793, 2513, 7437, 22287, 70051, 222883, 700213, 2195139, 6959869, 22252933, 71201129, 227826699, 731309001, 2356460041, 7609531843, 24603325189, 79677148959, 258535824775, 840291483835, 2734637778217, 8910389207081, 29069537051081

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OFFSET

0,4

COMMENTS

Diagonal of the rational function 1 / ((1-x)*(1-y)*(1-z) - x^2*y^3*z^3).

LINKS

Table of n, a(n) for n=0..29.

PROG

(PARI) a(n) = sum(k=0, n\3, binomial(n-k, k)*binomial(n-2*k, k)^2);

CROSSREFS

Sequence in context: A256316 A194486 A024535 * A196235 A120479 A146227

Adjacent sequences: A383574 A383575 A383576 * A383578 A383579 A383580

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 30 2025

STATUS

approved