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A250432 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A250432 #11 Jul 23 2025 12:24:28
%S A250432 16,36,36,81,108,81,144,324,324,144,256,720,1296,720,256,400,1600,
%T A250432 3600,3600,1600,400,625,3000,10000,12000,10000,3000,625,900,5625,
%U A250432 22500,40000,40000,22500,5625,900,1296,9450,50625,105000,160000,105000,50625,9450
%N A250432 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A250432 Table starts
%C A250432 ...16....36.....81.....144......256.......400.......625........900........1296
%C A250432 ...36...108....324.....720.....1600......3000......5625.......9450.......15876
%C A250432 ...81...324...1296....3600....10000.....22500.....50625......99225......194481
%C A250432 ..144...720...3600...12000....40000....105000....275625.....617400.....1382976
%C A250432 ..256..1600..10000...40000...160000....490000...1500625....3841600.....9834496
%C A250432 ..400..3000..22500..105000...490000...1715000...6002500...17287200....49787136
%C A250432 ..625..5625..50625..275625..1500625...6002500..24010000...77792400...252047376
%C A250432 ..900..9450..99225..617400..3841600..17287200..77792400..280052640..1008189504
%C A250432 .1296.15876.194481.1382976..9834496..49787136.252047376.1008189504..4032758016
%C A250432 .1764.24696.345744.2765952.22127616.124467840.700131600.3080579040.13554547776
%C A250432 Essentially the same as A202100; the mapping between the binary arrays in both sequences is by flipping all entries in one set of arrays. - _Joerg Arndt_, Dec 01 2014
%H A250432 R. H. Hardin, <a href="/A250432/b250432.txt">Table of n, a(n) for n = 1..1104</a>
%F A250432 Empirical for column k:
%F A250432 k=1: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8); also a polynomial of degree 4 plus a quasipolynomial of degree 2 with period 2
%F A250432 k=2: [order 12; also a polynomial of degree 6 plus a quasipolynomial of degree 4 with period 2]
%F A250432 k=3: [order 16; also a polynomial of degree 8 plus a quasipolynomial of degree 6 with period 2]
%F A250432 k=4: [order 20; also a polynomial of degree 10 plus a quasipolynomial of degree 8 with period 2]
%F A250432 k=5: [order 24; also a polynomial of degree 12 plus a quasipolynomial of degree 10 with period 2]
%F A250432 k=6: [order 28; also a polynomial of degree 14 plus a quasipolynomial of degree 12 with period 2]
%F A250432 k=7: [order 32; also a polynomial of degree 16 plus a quasipolynomial of degree 14 with period 2]
%e A250432 Some solutions for n=5 k=4
%e A250432 ..0..0..0..0..1....0..0..0..0..0....0..0..1..0..1....0..0..0..1..1
%e A250432 ..0..1..0..1..1....0..0..0..1..0....1..1..1..1..1....0..0..1..1..1
%e A250432 ..0..0..1..0..1....0..0..0..1..0....0..0..1..1..1....0..0..1..1..1
%e A250432 ..0..1..1..1..1....0..0..0..1..0....1..1..1..1..1....0..0..1..1..1
%e A250432 ..0..1..1..1..1....0..0..0..1..0....0..1..1..1..1....1..0..1..1..1
%e A250432 ..0..1..1..1..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
%Y A250432 Column 1 is A030179(n+3), A202093 - A202099 (further columns).
%K A250432 nonn,tabl
%O A250432 1,1
%A A250432 _R. H. Hardin_, Nov 22 2014