A042984 Number of n-dimensional partitions of 6.

1, 11, 48, 140, 326, 657, 1197, 2024, 3231, 4927, 7238, 10308, 14300, 19397, 25803, 33744, 43469, 55251, 69388, 86204, 106050, 129305, 156377, 187704, 223755, 265031, 312066, 365428, 425720, 493581, 569687, 654752, 749529, 854811, 971432

Offset

0,2

References

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(n) = A008780(n) - binomial(n, 4) - binomial(n, 3).

G.f.: (x^4 - 3*x^3 - 3*x^2 + 5*x + 1)/(x-1)^6. - Colin Barker, Jul 22 2012

a(n) = (n+1)*(n+4)*(n^3 + 40*n^2 + 61*n + 30)/120. - Robert Israel, Jul 06 2016

Maple

a:= n-> 1+10*n+27*binomial(n, 2)+28*binomial(n, 3)
              +11*binomial(n, 4)+binomial(n, 5):
seq(a(n), n=0..34);

Mathematica

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 11, 48, 140, 326, 657}, 40] (* Harvey P. Dale, Jan 27 2013 *)
CoefficientList[Series[(x^4 -3x^3 -3x^2 +5x +1)/(x-1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 27 2013 *)

Prog

(Magma) [1 + 10*n + 27*Binomial(n, 2) + 28*Binomial(n, 3) + 11*Binomial(n, 4) + Binomial(n, 5): n in [0..40]]; // Vincenzo Librandi, Oct 27 2013
(PARI) my(x='x+O('x^40)); Vec((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6) \\ G. C. Greubel, Feb 17 2019
(Sage) ((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 17 2019
(GAP) List([0..40], n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # Muniru A Asiru, Feb 17 2019

Crossrefs

Cf. A007326, A007327, A008780.

Sequence in context: A230982 A024530 A117066 * A364579 A008780 A211058

Adjacent sequences: A042981 A042982 A042983 * A042985 A042986 A042987

Keyword

nonn,easy

Author

Alford Arnold, Aug 15 1998

Extensions

More terms from Erich Friedman

Status

approved