cp's OEIS Frontend

A184701 Number of strings of numbers x(i=1..n) in 0..7 with sum i*x(i) equal to n*7.

%I A184701 #15 Aug 29 2022 10:04:40
%S A184701 1,4,22,107,471,1842,6575,21713,67105,195760,543050,1440869,3674381,
%T A184701 9042422,21548644,49872800,112387351,247136196,531320447,1118701390,
%U A184701 2310261518,4685733808,9345070552,18346037917,35487652677,67696833402
%N A184701 Number of strings of numbers x(i=1..n) in 0..7 with sum i*x(i) equal to n*7.
%C A184701 Column 7 of A184703.
%H A184701 Robert Israel, <a href="/A184701/b184701.txt">Table of n, a(n) for n = 1..1000</a> (first 139 terms from R. H. Hardin)
%e A184701 Some solutions for n=4
%e A184701 ..5....5....4....4....3....7....5....3....2....2....3....0....0....4....0....4
%e A184701 ..3....0....0....4....7....3....1....6....1....7....0....3....4....6....0....7
%e A184701 ..3....1....4....0....1....5....7....3....4....4....7....6....0....4....4....2
%e A184701 ..2....5....3....4....2....0....0....1....3....0....1....1....5....0....4....1
%p A184701 F:= proc(n,t) option remember; local d,s;
%p A184701   if n = 1 then return `if`(t<=7,1,0) fi;
%p A184701   s:= 0:
%p A184701   for d from 0 to min(7, t/n) do
%p A184701     s:= s + procname(n-1,t-n*d)
%p A184701   od:
%p A184701   s
%p A184701 end proc:
%p A184701 seq(F(n,7*n),n=1..100); # _Robert Israel_, Feb 13 2017
%t A184701 F[n_, t_] := F[n, t] = Module[{d, s}, If[n == 1, Return[If[t <= 7, 1, 0]]]; s = 0; For[d = 0, d <= Min[7, t/n], d++, s += F[n - 1, t - n*d]]; s];
%t A184701 Table[F[n, 7*n], {n, 1, 100}] (* _Jean-François Alcover_, Aug 29 2022, after _Robert Israel_ *)
%Y A184701 Cf. A184703.
%K A184701 nonn
%O A184701 1,2
%A A184701 _R. H. Hardin_, Jan 20 2011