A102422 Number of partitions of n with k <= 5 parts and each part p <= 5.

1, 1, 2, 3, 5, 7, 9, 11, 14, 16, 18, 19, 20, 20, 19, 18, 16, 14, 11, 9, 7, 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

Offset

0,3

Comments

There are only 26 nonzero terms.

Contribution from Toby Gottfried, Feb 19 2009: (Start)

a(n) is the number of partitions of n+5 into exactly 5 parts with each part p: 1 <= p <= 6

i.e. the number of different ways to get a total of n+5 with 5 (normal, 6-sided) dice in any order (End)

Links

Table of n, a(n) for n=0..98.

Formula

G.f.: = 1+z+2*z^2+3*z^3+5*z^4+7*z^5+9*z^6+11*z^7+14*z^8+16*z^9+18*z^10+19*z^11+20*z^12+20*z^13+19*z^14+18*z^15+16*z^16+14*z^17+11*z^18+9*z^19 +7*z^20+5*z^21+3*z^22+2*z^23+z^24+z^25.

Example

a(7)=11 because we can write 7=1+2+2+2 or 5+2 or 1+2+4 or 3+4 or 1+3+3 or 1+1+1+1+3 or 1+1+2+3 or 2+2+3 or 1+1+1+2+2 1+1+1+4 or 1+1+5.
A total of 8 comes from 1+1+1+1+4, 1+1+1+2+3, 1+1+2+2+2 and a(3) = 3 [8 = 3+5] [From Toby Gottfried, Feb 19 2009]

Crossrefs

See A102420 for k=5 and p<=5.

Cf. A000041, A102420, A063746.

Contribution from Toby Gottfried, Feb 19 2009: (Start)

A102420 has the numbers for 4 dice

A063260 gives the number of permuted rolls of each possible total for any number of dice. (End)

Sequence in context: A024678 A265384 A039786 * A062427 A127721 A292620

Adjacent sequences: A102419 A102420 A102421 * A102423 A102424 A102425

Keyword

easy,nonn

Author

Thomas Wieder, Jan 09 2005

Status

approved