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A254567 Number of (n+2)X(7+2) 0..1 arrays with every 3X3 subblock sum of the four sums of the central row, central column, diagonal and antidiagonal nondecreasing horizontally and vertically 1

%I

%S 1029664,4205934,20277514,25618602,45085796,120967261,206491388,

%T 496247824,980309768,2140733638,4396657758,9138690014,18508554954,

%U 37124963771,73186116528,142299121992,272494928124,514557580661

%N Number of (n+2)X(7+2) 0..1 arrays with every 3X3 subblock sum of the four sums of the central row, central column, diagonal and antidiagonal nondecreasing horizontally and vertically

%C Column 7 of A254568

%H R. H. Hardin, <a href="/A254567/b254567.txt">Table of n, a(n) for n = 1..210</a>

%H R. H. Hardin, <a href="/A254567/a254567.txt">polynomial of degree 25 plus a quasipolynomial of degree 12 with period 6 </a>

%F Empirical: a(n) = 12*a(n-1) -65*a(n-2) +221*a(n-3) -585*a(n-4) +1417*a(n-5) -3211*a(n-6) +6513*a(n-7) -12077*a(n-8) +21515*a(n-9) -36465*a(n-10) +57421*a(n-11) -86164*a(n-12) +125685*a(n-13) -173900*a(n-14) +227240*a(n-15) -288561*a(n-16) +353704*a(n-17) -407485*a(n-18) +449085*a(n-19) -481403*a(n-20) +483197*a(n-21) -446589*a(n-22) +391963*a(n-23) -311740*a(n-24) +190905*a(n-25) -60632*a(n-26) -60632*a(n-27) +190905*a(n-28) -311740*a(n-29) +391963*a(n-30) -446589*a(n-31) +483197*a(n-32) -481403*a(n-33) +449085*a(n-34) -407485*a(n-35) +353704*a(n-36) -288561*a(n-37) +227240*a(n-38) -173900*a(n-39) +125685*a(n-40) -86164*a(n-41) +57421*a(n-42) -36465*a(n-43) +21515*a(n-44) -12077*a(n-45) +6513*a(n-46) -3211*a(n-47) +1417*a(n-48) -585*a(n-49) +221*a(n-50) -65*a(n-51) +12*a(n-52) -a(n-53) for n>71

%F polynomial of degree 25 plus a quasipolynomial of degree 12 with period 6 for n>18 (see link above)

%e Some solutions for n=1

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 01 2015

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Last modified February 4 02:26 EST 2023. Contains 360045 sequences. (Running on oeis4.)