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Number of (n+3) X (1+3) 0..1 arrays with no 4x4 4 X 4 subblock diagonal sum less than the antidiagonal sum.

Column 1 of A258689.

Empirical: a(n) = 16*a(n-1) -93*a(n-2) +336*a(n-3) -1824*a(n-4) +8792*a(n-5) -23538*a(n-6) +77820*a(n-7) -332915*a(n-8) +734418*a(n-9) -1635264*a(n-10) +6618544*a(n-11) -12488383*a(n-12) +18555412*a(n-13) -76246952*a(n-14) +127021008*a(n-15) -117094208*a(n-16) +528259472*a(n-17) -807573040*a(n-18) +402922176*a(n-19) -2172435648*a(n-20) +3192355184*a(n-21) -662848288*a(n-22) +4910710016*a(n-23) -7229424768*a(n-24) -12698624*a(n-25) -5017550272*a(n-26) +7380494976*a(n-27) +2914034432*a(n-28) +542097920*a(n-29) -1263132608*a(n-30) -5725840384*a(n-31) +2030375680*a(n-32) +256829440*a(n-33) +204132352*a(n-34) +1616855040*a(n-35) -1361873920*a(n-36) +476446720*a(n-37) +102010880*a(n-38) -484499456*a(n-39) +282083328*a(n-40) -25362432*a(n-41) -53673984*a(n-42) +46792704*a(n-43) -16777216*a(n-44) +2097152*a(n-45).

Cf. A258689.

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R. H. Hardin, <a href="/A258685/b258685.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of (n+3)X(1+3) 0..1 arrays with no 4x4 subblock diagonal sum less than the antidiagonal sum

41728, 386304, 3512272, 27566112, 202381312, 1439941888, 9687764256, 62708952320, 395604998544, 2427405266624, 14557211699776, 85740787849600, 496635767096000, 2835034400071040, 15984403484875664, 89126750206019424

1,1

Column 1 of A258689

Empirical: a(n) = 16*a(n-1) -93*a(n-2) +336*a(n-3) -1824*a(n-4) +8792*a(n-5) -23538*a(n-6) +77820*a(n-7) -332915*a(n-8) +734418*a(n-9) -1635264*a(n-10) +6618544*a(n-11) -12488383*a(n-12) +18555412*a(n-13) -76246952*a(n-14) +127021008*a(n-15) -117094208*a(n-16) +528259472*a(n-17) -807573040*a(n-18) +402922176*a(n-19) -2172435648*a(n-20) +3192355184*a(n-21) -662848288*a(n-22) +4910710016*a(n-23) -7229424768*a(n-24) -12698624*a(n-25) -5017550272*a(n-26) +7380494976*a(n-27) +2914034432*a(n-28) +542097920*a(n-29) -1263132608*a(n-30) -5725840384*a(n-31) +2030375680*a(n-32) +256829440*a(n-33) +204132352*a(n-34) +1616855040*a(n-35) -1361873920*a(n-36) +476446720*a(n-37) +102010880*a(n-38) -484499456*a(n-39) +282083328*a(n-40) -25362432*a(n-41) -53673984*a(n-42) +46792704*a(n-43) -16777216*a(n-44) +2097152*a(n-45)

Some solutions for n=1

..0..0..0..1....1..0..1..0....1..0..0..1....1..0..1..1....1..0..1..1

..1..0..0..1....1..0..0..1....1..1..0..0....0..1..1..1....1..0..0..0

..0..1..1..0....1..0..1..1....0..0..1..1....0..1..1..1....0..0..1..0

..0..0..1..1....1..0..1..1....1..0..0..0....1..1..0..1....0..0..0..0

Cf. A258689

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nonn

R. H. Hardin, Jun 07 2015

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