A327842 Number of colored integer partitions of n using all colors of a 3-set such that a color pattern for part i has i distinct colors in increasing order.

5, 18, 45, 94, 174, 300, 486, 756, 1131, 1647, 2334, 3243, 4416, 5922, 7818, 10195, 13128, 16734, 21110, 26403, 32736, 40291, 49221, 59748, 72060, 86424, 103068, 122310, 144423, 169782, 198711, 231648, 268974, 311197, 358761, 412251, 472181, 539220, 613959

Offset: 3

Author

Alois P. Heinz, Sep 27 2019

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..10000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-7,3,6,0,-6,-3,7,0,-3,1).

Crossrefs

Column k=3 of A327117.

Formula

G.f.: -(x^9-6*x^7+x^6+9*x^5+3*x^4-6*x^3-9*x^2+3*x+5)*x^3 / ((x^2+x+1) *(x+1)^3 *(x-1)^7).