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A028346 Expansion of 1/((1-x)^4*(1-x^2)^2). 3
1, 4, 12, 28, 58, 108, 188, 308, 483, 728, 1064, 1512, 2100, 2856, 3816, 5016, 6501, 8316, 10516, 13156, 16302, 20020, 24388, 29484, 35399, 42224, 50064, 59024, 69224, 80784, 93840, 108528, 125001, 143412, 163932, 186732, 212002, 239932, 270732, 304612, 341803 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=0..40.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,10,-4,-4,4,-1).

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

From Antal Pinter, Jan 08 2016: (Start)

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

a(n) = Sum_{i = 1..z} i*C(n + 5 - 2*i,3) where z = (2*n + 3 + (-1)^n)/4.

(End)

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

MATHEMATICA

CoefficientList[Series[1/((1 - x)^4 (1 - x^2)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Feb 14 2016 *)

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

PROG

(PARI) Vec(1/((1-x)^4*(1-x^2)^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

(MAGMA) [(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

CROSSREFS

Cf. A152205, A001752 (for the similar series 1/((1-x)^4*(1-x^2))).

Sequence in context: A102650 A011939 A203286 * A079089 A182705 A186924

Adjacent sequences:  A028343 A028344 A028345 * A028347 A028348 A028349

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 10 19:52 EDT 2020. Contains 336381 sequences. (Running on oeis4.)