A184705 Number of strings of numbers x(i=1..5) in 0..n with sum i*x(i) equal to n*5.
3, 12, 34, 78, 156, 282, 471, 744, 1119, 1623, 2279, 3118, 4167, 5463, 7039, 8935, 11188, 13845, 16946, 20545, 24685, 29424, 34812, 40911, 47775, 55472, 64060, 73612, 84190, 95874, 108729, 122840, 138277, 155129, 173473, 193402, 214995, 238353
Offset: 1
Keywords
Examples
Some solutions for n=3: ..0....0....3....1....2....2....2....3....0....0....1....2....1....2....2....1 ..1....2....1....1....2....1....0....0....2....0....2....0....2....0....2....0 ..1....1....2....1....3....1....3....1....2....2....2....1....0....0....0....2 ..0....2....1....1....0....2....1....1....0....1....1....0....0....2....1....2 ..2....0....0....1....0....0....0....1....1....1....0....2....2....1....1....0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..200
Crossrefs
Cf. A184703.
Formula
Empirical: a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15).
Empirical g.f.: x*(3 + 9*x + 19*x^2 + 32*x^3 + 44*x^4 + 51*x^5 + 48*x^6 + 40*x^7 + 25*x^8 + 13*x^9 + 4*x^10 + x^11 - x^12 - x^13 + x^14) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 14 2018
Comments