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 A258890 Number of (n+2) X (4+2) 0..1 arrays with no 3 x 3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum. 1

%I #8 Dec 22 2018 11:31:46

%S 10201,10680,8100,7225,9604,13221,17424,23393,30276,39565,50176,63945,

%T 79524,99125,121104,148081,178084,214173,254016,301145,352836,413125,

%U 478864,554625,636804,730541,831744,946153,1069156,1207125,1354896

%N Number of (n+2) X (4+2) 0..1 arrays with no 3 x 3 subblock diagonal sum less than the antidiagonal sum or central row sum less than the central column sum.

%H R. H. Hardin, <a href="/A258890/b258890.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: 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) for n>11.

%F Empirical for n mod 2 = 0: a(n) = n^4 + 10*n^3 + 122*n^2 + 498*n + 2385 for n>3.

%F Empirical for n mod 2 = 1: a(n) = n^4 + 10*n^3 + 121*n^2 + 480*n + 2304 for n>3.

%F Empirical g.f.: x*(10201 - 9722*x - 33662*x^2 + 30871*x^3 + 43034*x^4 - 33043*x^5 - 28554*x^6 + 12889*x^7 + 11977*x^8 - 883*x^9 - 2916*x^10) / ((1 - x)^5*(1 + x)^3). - _Colin Barker_, Dec 22 2018

%e Some solutions for n=4:

%e ..0..1..0..0..0..1....0..1..0..1..0..1....1..0..0..0..0..0....1..0..1..0..0..1

%e ..1..1..0..1..0..0....1..1..1..1..1..0....1..0..0..0..0..0....1..1..0..1..0..1

%e ..1..0..1..0..1..1....1..1..1..1..1..1....0..0..0..0..0..1....1..0..1..0..1..1

%e ..1..1..0..1..0..1....1..1..1..1..1..1....0..0..0..0..0..0....0..1..0..1..0..1

%e ..1..0..1..0..1..1....0..1..1..1..1..1....0..0..0..0..0..1....0..0..1..0..1..1

%e ..0..1..0..1..0..1....1..0..1..1..1..1....0..0..0..0..0..1....0..0..0..0..1..1

%Y Column 4 of A258894.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 14 2015

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Last modified February 24 17:27 EST 2024. Contains 370307 sequences. (Running on oeis4.)