A233302 Number of (2+1) X (n+1) 0..1 arrays x(i,j) with row sums sum{x(i,j), j=1..n+1} nondecreasing, and column sums sum{i^2*x(i,j), i=1..2+1} nondecreasing.
15, 42, 105, 232, 475, 904, 1632, 2806, 4642, 7414, 11500, 17368, 25636, 37054, 52579, 73354, 100799, 136586, 182749, 241654, 316129, 409430, 525392, 668390, 843514, 1056524, 1314050, 1623542, 1993496, 2433398, 2953979, 3567152, 4286297, 5126192
Offset: 1
Keywords
Examples
Some solutions for n=5: ..0..0..0..0..1..0....1..1..0..0..0..0....0..0..1..0..0..0....0..0..0..0..0..1 ..0..0..0..0..0..1....0..0..1..1..1..1....0..0..0..0..0..1....0..1..1..1..1..1 ..0..0..0..1..1..1....0..1..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..172
Formula
Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - 7*a(n-3) + 10*a(n-4) + 3*a(n-5) - 6*a(n-6) - 6*a(n-7) + 3*a(n-8) + 10*a(n-9) - 7*a(n-10) - 3*a(n-11) + 4*a(n-12) - a(n-13). - R. H. Hardin, Jan 17 2016.
Empirical g.f.: x*(15 - 18*x - 18*x^2 + 43*x^3 + 6*x^4 - 30*x^5 - 21*x^6 + 22*x^7 + 33*x^8 - 31*x^9 - 8*x^10 + 15*x^11 - 4*x^12) / ((1 - x)^8*(1 + x)^3*(1 + x + x^2)). - Colin Barker, Mar 19 2018
Comments