|
%I #7 Dec 12 2018 03:22:48
%S 1,7,28,42,168,238,280,428,595,595,826,910,1078,1232,1716,1498,2023,
%T 2093,2450,2450,2996,3228,3626,3710,4193,4263,4998,4928,5916,5838,
%U 6426,6510,7371,7455,8316,8464,9198,9268,10318,10248,11319,11473,12524,12460,13636
%N Number of compositions of n into parts with distinct multiplicities and with exactly seven parts.
%H Alois P. Heinz, <a href="/A321777/b321777.txt">Table of n, a(n) for n = 7..1000</a>
%F Conjectures from _Colin Barker_, Dec 11 2018: (Start)
%F 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)).
%F 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.
%F (End)
%Y Column k=7 of A242887.
%K nonn
%O 7,2
%A _Alois P. Heinz_, Nov 18 2018
|
