The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A028346

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A028346

Expansion of 1/((1-x)^4*(1-x^2)^2).
(history; published version)

#39 by Jon E. Schoenfield at Sat Feb 05 15:45:31 EST 2022

STATUS

editing

approved

#38 by Jon E. Schoenfield at Sat Feb 05 15:45:26 EST 2022

COMMENTS

Equals triangle A152205 as an infinite lower triangular matrix * the triangular numbers: [1, 3, 6, ...]. - Gary W. Adamson, Feb 14 2010

FORMULA

a(n) = (n+4)*(2*n^4 + 32*n^3 + 172*n^2 + 352*n + 15*(-1)^n + 225)/960. - R. J. Mathar, Apr 01 2010

PROG

(MAGMAMagma) [(n+4)*(2*n^4+32*n^3+172*n^2+352*n+15*(-1)^n+225)/960: n in [0..40]]; // Vincenzo Librandi, Feb 14 2016

STATUS

approved

editing

#37 by Bruno Berselli at Fri Nov 25 02:42:48 EST 2016

STATUS

editing

approved

#36 by Bruno Berselli at Fri Nov 25 02:42:44 EST 2016

LINKS

<a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (4, -4, -4, 10, -4, -4, 4, -1).

MATHEMATICA

LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {1, 4, 12, 28, 58, 108, 188, 308}, 100] (* _G. C. Greubel_, Nov 25 2016 *)

108, 188, 308}, 100] (* G. C. Greubel, Nov 25 2016 *)

STATUS

proposed

editing

#35 by G. C. Greubel at Fri Nov 25 02:36:56 EST 2016

STATUS

editing

proposed

#34 by G. C. Greubel at Fri Nov 25 02:36:43 EST 2016

COMMENTS

a(n) is the number of partitions of n into four kinds of parts 1 and two kinds of parts 2. [_- _Joerg Arndt_, Mar 09 2016]

FORMULA

a(n) = (n+4)*(2*n^4 +32*n^3 +172*n^2 +352*n +15*(-1)^n +225)/960. [_- _R. J. Mathar_, Apr 01 2010]

MATHEMATICA

LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {1, 4, 12, 28, 58,

108, 188, 308}, 100] (* G. C. Greubel, Nov 25 2016 *)

AUTHOR

N. J. A. Sloane.

STATUS

approved

editing

#33 by Bruno Berselli at Fri May 06 02:38:41 EDT 2016

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reviewed

approved

#32 by Joerg Arndt at Fri May 06 02:16:54 EDT 2016

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proposed

reviewed

#31 by Antal Pinter at Thu May 05 20:34:40 EDT 2016

STATUS

editing

proposed

#30 by Antal Pinter at Thu May 05 20:31:05 EDT 2016

FORMULA

a(n) = Sum_{i = 0..n} A002624(i). - Antal Pinter, May 05 2016

STATUS

approved

editing