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A250429 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.

%I A250429 #10 Jul 23 2025 12:24:06
%S A250429 256,1600,10000,40000,160000,490000,1500625,3841600,9834496,22127616,
%T A250429 49787136,101606400,207360000,392040000,741200625,1317690000,
%U A250429 2342560000,3958926400,6690585616,10837642816,17555190016,27429984400,42859350625
%N A250429 Number of (n+1)X(5+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
%C A250429 Column 5 of A250432.
%H A250429 R. H. Hardin, <a href="/A250429/b250429.txt">Table of n, a(n) for n = 1..210</a>
%F A250429 Empirical: a(n) = 2*a(n-1) +10*a(n-2) -22*a(n-3) -44*a(n-4) +110*a(n-5) +110*a(n-6) -330*a(n-7) -165*a(n-8) +660*a(n-9) +132*a(n-10) -924*a(n-11) +924*a(n-13) -132*a(n-14) -660*a(n-15) +165*a(n-16) +330*a(n-17) -110*a(n-18) -110*a(n-19) +44*a(n-20) +22*a(n-21) -10*a(n-22) -2*a(n-23) +a(n-24)
%F A250429 Empirical for n mod 2 = 0: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (407/1327104)*n^10 + (275/55296)*n^9 + (5933/110592)*n^8 + (415/1024)*n^7 + (182201/82944)*n^6 + (3715/432)*n^5 + (62483/2592)*n^4 + (2545/54)*n^3 + (731/12)*n^2 + (140/3)*n + 16
%F A250429 Empirical for n mod 2 = 1: a(n) = (1/5308416)*n^12 + (5/442368)*n^11 + (817/2654208)*n^10 + (2225/442368)*n^9 + (97157/1769472)*n^8 + (3455/8192)*n^7 + (3101111/1327104)*n^6 + (2080805/221184)*n^5 + (144963631/5308416)*n^4 + (24654385/442368)*n^3 + (7461475/98304)*n^2 + (3044125/49152)*n + (1500625/65536).
%F A250429 a(n+1) = A202096(n). - _R. J. Mathar_, Dec 02 2014
%e A250429 Some solutions for n=5
%e A250429 ..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..1....0..0..0..0..0..1
%e A250429 ..0..0..1..1..1..1....0..0..0..0..1..1....0..0..0..0..1..1....0..0..1..0..1..0
%e A250429 ..0..0..0..0..0..0....1..0..1..1..1..1....0..0..0..0..0..1....0..0..0..1..1..1
%e A250429 ..0..0..1..1..1..1....1..0..1..0..1..1....0..0..0..1..1..1....0..0..1..1..1..1
%e A250429 ..0..0..0..1..0..1....1..0..1..1..1..1....0..0..0..1..0..1....1..1..1..1..1..1
%e A250429 ..1..0..1..1..1..1....1..1..1..1..1..1....0..0..0..1..1..1....0..0..1..1..1..1
%K A250429 nonn
%O A250429 1,1
%A A250429 _R. H. Hardin_, Nov 22 2014