A321777 Number of compositions of n into parts with distinct multiplicities and with exactly seven parts.

1, 7, 28, 42, 168, 238, 280, 428, 595, 595, 826, 910, 1078, 1232, 1716, 1498, 2023, 2093, 2450, 2450, 2996, 3228, 3626, 3710, 4193, 4263, 4998, 4928, 5916, 5838, 6426, 6510, 7371, 7455, 8316, 8464, 9198, 9268, 10318, 10248, 11319, 11473, 12524, 12460, 13636

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

Conjectures from Colin Barker, Dec 11 2018: (Start)

G.f.: x^7*(1 + 8*x + 36*x^2 + 78*x^3 + 245*x^4 + 475*x^5 + 719*x^6 + 1069*x^7 + 1419*x^8 + 1539*x^9 + 1645*x^10 + 1478*x^11 + 1100*x^12 + 708*x^13 + 505*x^14) / ((1 - x)^3*(1 + x)^2*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

a(n) = -a(n-1) - a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) + 3*a(n-7) + 3*a(n-8) + 2*a(n-9) + a(n-10) - a(n-11) - 2*a(n-12) - 3*a(n-13) - 3*a(n-14) - 2*a(n-15) - a(n-16) + a(n-18) + a(n-19) + a(n-20) + a(n-21) for n>27.

(End)

Crossrefs

Column k=7 of A242887.

Sequence in context: A155712 A015817 A103253 * A269451 A139607 A068206

Adjacent sequences: A321774 A321775 A321776 * A321778 A321779 A321780

Keyword

nonn

Author

Alois P. Heinz, Nov 18 2018

Status

approved