OFFSET
0,2
COMMENTS
Number of partitions of 60n+k, 0<=k<60 into parts <=6 is a polynomial of degree 5 by variable n.
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = 1 +(167*n +2325*n^2 +15400*n^3 +47250*n^4 +54000*n^5)/6.
a(n) = A001402(60*n).
G.f.: (3331*x^5+161052*x^4+578757*x^3+317007*x^2+19852*x+1)/(x-1)^6. [Colin Barker, Jan 31 2013]
MATHEMATICA
Table[1 + (167n + 2325n^2 + 15400n^3 + 47250n^4 + 54000n^5)/6, {n, 0, 25}]
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 19858, 436140, 2897747, 11402579, 33377536}, 30] (* Harvey P. Dale, Aug 12 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Aug 21 2011
STATUS
approved