A258685 - OEIS

%I #7 Mar 08 2023 11:47:57

%S 41728,386304,3512272,27566112,202381312,1439941888,9687764256,

%T 62708952320,395604998544,2427405266624,14557211699776,85740787849600,

%U 496635767096000,2835034400071040,15984403484875664,89126750206019424

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

%C Column 1 of A258689.

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

%F 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).

%e Some solutions for n=1

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

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

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

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

%Y Cf. A258689.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 07 2015