A102420 Number of partitions of n into exactly k = 5 parts with each part p <= 5.

0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 8, 9, 11, 11, 12, 11, 11, 9, 8, 6, 5, 3, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,8

Comments

There are only 26 nonzero terms.

a(n) is also the number of partitions of n-1 into exactly 4 parts with each part p in the range 1 <= p <= 6; i.e. the number of ways of arriving at a total of n-1 with 4 6-sided dice. - Toby Gottfried, Feb 19 2009

Links

Table of n, a(n) for n=0..102.

Formula

G.f.:z^5+z^6+2*z^7+3*z^8+5*z^9+6*z^10+8*z^11+9*z^12+11*z^13 +11*z^14 +12*z^15+ 11*z^16+11*z^17+9*z^18+8*z^19+6*z^20+5*z^21+3*z^22 +2*z^23 +z^24 +z^25.

Example

a(8) = 3 because we can write 8=1+1+1+2+3 or 1+1+1+1+4 or 1+1+2+2+2.

Mathematica

Table[Count[IntegerPartitions[n, {5}], _?(Max[#]<6&)], {n, 0, 110}] (* Harvey P. Dale, Nov 29 2012 *)

Crossrefs

Cf. A000041, A102422, A036606.

Sequence in context: A098161 A026194 A289279 * A036606 A051837 A026371

Adjacent sequences: A102417 A102418 A102419 * A102421 A102422 A102423

Keyword

easy,nonn

Author

Thomas Wieder, Jan 09 2005

Status

approved