The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A360314 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A360314

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,n-3*k) * binomial(2*k,k).
(history; published version)

#10 by Michael De Vlieger at Fri Feb 03 08:17:48 EST 2023

STATUS

proposed

approved

#9 by Seiichi Manyama at Fri Feb 03 07:15:59 EST 2023

STATUS

editing

proposed

#8 by Seiichi Manyama at Fri Feb 03 02:19:52 EST 2023

CROSSREFS

Cf. A360294, A360309.

#7 by Seiichi Manyama at Fri Feb 03 01:43:56 EST 2023

DATA

1, 0, 0, -2, -2, -2, 4, 10, 16, 2, -32, -86, -90, 26, 332, 646, 534, -690, -3040, -4934, -2270, 9066, 27260, 35198, 532, -101946, -232752, -230730, 158986, 1039078, 1899364, 1265370, -2714160, -9926158, -14625008, -4036358, 34062386, 89744810, 104123084

#6 by Seiichi Manyama at Fri Feb 03 01:40:37 EST 2023

FORMULA

G.f.: 1 / sqrt(1+4*x^3/(1-x)).

PROG

(PARI) a(n) = sum(k=0, n\3, (-1)^k*binomial(n-1-2*k, n-3*k)*binomial(2*k, k));

(PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^3/(1-x)))

#5 by Seiichi Manyama at Fri Feb 03 01:37:25 EST 2023

FORMULA

n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-3)*a(n-3) + 2*(2*n-6)*a(n-4).

#4 by Seiichi Manyama at Fri Feb 03 01:37:02 EST 2023

FORMULA

n*a(n) = 2*(n-1)*a(n-1) -(n-2)*a(n-2)-2*(2*n-3)*a(n-3) + 2*(2*n-6)*a(n-4).

#3 by Seiichi Manyama at Fri Feb 03 01:26:25 EST 2023

CROSSREFS

Cf. A360313, A360315.

#2 by Seiichi Manyama at Fri Feb 03 01:23:08 EST 2023

NAME

allocated for Seiichi Manyama

a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(n-1-2*k,n-3*k) * binomial(2*k,k).

DATA

1, 0, 0, -2, -2, -2, 4, 10, 16, 2, -32, -86, -90, 26, 332, 646

OFFSET

0,4

KEYWORD

allocated

sign

AUTHOR

Seiichi Manyama, Feb 03 2023

STATUS

approved

editing

#1 by Seiichi Manyama at Fri Feb 03 01:23:08 EST 2023

NAME

allocated for Seiichi Manyama

KEYWORD

allocated

STATUS

approved