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

Author

Alford Arnold, Aug 15 1998

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A007326, A007327, A008780.

Programs

GAP

List([0..40],n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # Muniru A Asiru, Feb 17 2019

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

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 *)

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

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

Extensions

More terms from Erich Friedman