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A069982 Number of 4-gonal compositions of n into positive parts. 2
0, 0, 0, 0, 1, 4, 10, 16, 31, 40, 68, 80, 125, 140, 206, 224, 315, 336, 456, 480, 633, 660, 850, 880, 1111, 1144, 1420, 1456, 1781, 1820, 2198, 2240, 2675, 2720, 3216, 3264, 3825, 3876, 4506, 4560, 5263, 5320, 6100, 6160, 7021, 7084, 8030 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III. The Omega package, p. 17.

G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis: The Omega Package, European Journal of Combinatorics, Vol. 22, No. 7 (2001), 887-904.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

FORMULA

G.f.: q^4/(1-q)^4-4*q^7/(1-q)^4/(1+q)^3.

a(n) = (2*n^3-3*n^2-23*n+3*(13+(n^2-7*n+11)*(-1)^n))/24. - Luce ETIENNE, Jul 02 2015; edited by Mo Li, Sep 18 2019

a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7) for n>7. - Colin Barker, Sep 18 2019

MATHEMATICA

Table[Piecewise[{

   {Binomial[k - 1, k - 4] - 4*Binomial[(k - 1)/2, (k - 7)/2], Mod[k, 2] == 1},

   {Binomial[k - 1, k - 4] - 4*Binomial[(k - 2)/2, (k - 8)/2], Mod[k, 2] == 0}}], {k, 1, 20}] (* Mo Li, Sep 18 2019 *)

PROG

(PARI) concat([0, 0, 0, 0], Vec(x^4*(1 + 3*x + 3*x^2 - 3*x^3) / ((1 - x)^4*(1 + x)^3) + O(x^40))) \\ Colin Barker, Sep 18 2019

CROSSREFS

Cf. A069981, A069983, A005044.

Sequence in context: A027425 A024992 A224966 * A009883 A333904 A163389

Adjacent sequences:  A069979 A069980 A069981 * A069983 A069984 A069985

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 06 2002

STATUS

approved

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Last modified April 16 23:40 EDT 2021. Contains 343051 sequences. (Running on oeis4.)