The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A371871 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A371871

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

#11 by R. J. Mathar at Mon Apr 22 12:31:04 EDT 2024

STATUS

editing

approved

#10 by R. J. Mathar at Mon Apr 22 12:30:52 EDT 2024

MAPLE

A371871 := proc(n)

1/(1-x^3)/(1-x)^(n-1) ;

coeftayl(%, x=0, n) ;

end proc:

seq(A371871(n), n=0..60) ; # R. J. Mathar, Apr 22 2024

#9 by R. J. Mathar at Mon Apr 22 12:30:13 EDT 2024

FORMULA

D-finite with recurrence 9*n*a(n) +3*(-17*n+16)*a(n-1) +3*(21*n-50)*a(n-2) +(-17*n+16)*a(n-3) +10*(2*n-5)*a(n-4)=0. - R. J. Mathar, Apr 22 2024

STATUS

approved

editing

#8 by Michael De Vlieger at Wed Apr 10 08:44:18 EDT 2024

STATUS

proposed

approved

#7 by Seiichi Manyama at Wed Apr 10 08:10:39 EDT 2024

STATUS

editing

proposed

#6 by Seiichi Manyama at Wed Apr 10 08:10:35 EDT 2024

CROSSREFS

Cf. A105872, A371758.

STATUS

proposed

editing

#5 by Seiichi Manyama at Wed Apr 10 07:31:45 EDT 2024

STATUS

editing

proposed

#4 by Seiichi Manyama at Wed Apr 10 01:43:10 EDT 2024

DATA

1, 0, 1, 5, 18, 66, 246, 924, 3493, 13277, 50697, 194327, 747319, 2882061, 11142027, 43167573, 167561586, 651513594, 2537041938, 9892847952, 38623197264, 150959213886, 590626854072, 2312979822738, 9065733950526, 35561306875380, 139595183125750

#3 by Seiichi Manyama at Wed Apr 10 01:30:49 EDT 2024

CROSSREFS

Cf. A360150, A371872, A371873.

#2 by Seiichi Manyama at Wed Apr 10 01:25:12 EDT 2024

NAME

allocated for Seiichi Manyama

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

DATA

1, 0, 1, 5, 18, 66, 246, 924, 3493, 13277, 50697, 194327, 747319, 2882061, 11142027, 43167573, 167561586, 651513594, 2537041938, 9892847952, 38623197264, 150959213886, 590626854072, 2312979822738

OFFSET

0,4

FORMULA

a(n) = [x^n] 1/((1-x^3) * (1-x)^(n-1)).

PROG

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

CROSSREFS

Cf. A360150.

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Apr 10 2024

STATUS

approved

editing