cp's OEIS Frontend

A223999 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

%I A223999 #6 Jul 23 2025 04:49:14
%S A223999 3,6,9,10,31,27,15,76,157,81,21,155,476,793,243,28,281,1144,2980,4004,
%T A223999 729,36,469,2403,7927,18672,20216,2187,45,736,4614,17929,55333,117386,
%U A223999 102069,6561,55,1101,8291,36845,132119,388598,739672,515338,19683,66
%N A223999 T(n,k)=Number of nXk 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
%C A223999 Table starts
%C A223999 .....3........6........10........15.........21.........28..........36
%C A223999 .....9.......31........76.......155........281........469.........736
%C A223999 ....27......157.......476......1144.......2403.......4614........8291
%C A223999 ....81......793......2980......7927......17929......36845.......71061
%C A223999 ...243.....4004.....18672.....55333.....132119.....281271......559188
%C A223999 ...729....20216....117386....388598.....984595....2160036.....4368458
%C A223999 ..2187...102069....739672...2743444....7400832...16795265....34534687
%C A223999 ..6561...515338...4664776..19437479...55978489..131782267...276286000
%C A223999 .19683..2601899..29428242.138010718..425257387.1040869367..2229871293
%C A223999 .59049.13136773.185670484.981047716.3240026429.8260503068.18115082917
%H A223999 R. H. Hardin, <a href="/A223999/b223999.txt">Table of n, a(n) for n = 1..449</a>
%F A223999 Empirical: columns k=1..7 have recurrences of order 1,3,9,18,28,39,54 for n>0,0,0,19,31,44,61
%F A223999 Empirical: rows n=1..7 are polynomials of degree 2*n for k>0,0,2,4,6,8,10
%e A223999 Some solutions for n=3 k=4
%e A223999 ..0..0..0..1....1..1..2..2....0..0..0..0....2..2..2..2....0..0..0..0
%e A223999 ..0..1..2..2....0..1..1..2....0..0..2..2....0..2..2..2....0..0..2..2
%e A223999 ..2..2..2..2....0..0..1..2....0..0..1..2....2..2..2..2....2..2..2..2
%Y A223999 Column 1 is A000244
%Y A223999 Column 2 is A038223
%Y A223999 Row 1 is A000217(n+1)
%K A223999 nonn,tabl
%O A223999 1,1
%A A223999 _R. H. Hardin_ Mar 30 2013