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

1, 4, 22, 107, 471, 1842, 6575, 21713, 67105, 195760, 543050, 1440869, 3674381, 9042422, 21548644, 49872800, 112387351, 247136196, 531320447, 1118701390, 2310261518, 4685733808, 9345070552, 18346037917, 35487652677, 67696833402

Offset

1,2

Comments

Column 7 of A184703.

Links

Robert Israel, Table of n, a(n) for n = 1..1000 (first 139 terms from R. H. Hardin)

Example

Some solutions for n=4
..5....5....4....4....3....7....5....3....2....2....3....0....0....4....0....4
..3....0....0....4....7....3....1....6....1....7....0....3....4....6....0....7
..3....1....4....0....1....5....7....3....4....4....7....6....0....4....4....2
..2....5....3....4....2....0....0....1....3....0....1....1....5....0....4....1

Maple

F:= proc(n, t) option remember; local d, s;
  if n = 1 then return `if`(t<=7, 1, 0) fi;
  s:= 0:
  for d from 0 to min(7, t/n) do
    s:= s + procname(n-1, t-n*d)
  od:
  s
end proc:
seq(F(n, 7*n), n=1..100); # Robert Israel, Feb 13 2017

Mathematica

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];
Table[F[n, 7*n], {n, 1, 100}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)

Crossrefs

Cf. A184703.

Sequence in context: A220740 A099013 A184510 * A001436 A224243 A024420

Adjacent sequences: A184698 A184699 A184700 * A184702 A184703 A184704

Keyword

nonn

Author

R. H. Hardin, Jan 20 2011

Status

approved