A234328 - OEIS

A234328

Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).

%I #6 Jun 19 2022 02:22:46

%S 2368,25728,287888,3271560,37234216,425662432,4858165384,55631535036,

%T 635692080136,7287762748412,83358262956160,956674989178676,

%U 10953011278383544,125838143389011112,1442087851946088992

%N Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234328/b234328.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 507*a(n-2) -102295*a(n-4) +10646830*a(n-6) -635915377*a(n-8) +23832852746*a(n-10) -596280829182*a(n-12) +10371633339873*a(n-14) -128744093807520*a(n-16) +1159671655063068*a(n-18) -7660667577596808*a(n-20) +37368059037902308*a(n-22) -135219186772494408*a(n-24) +364034788822163472*a(n-26) -730004249849579520*a(n-28) +1089413122161376064*a(n-30) -1205481757762071168*a(n-32) +981742220067000064*a(n-34) -581000394777277440*a(n-36) +244895745327540224*a(n-38) -71316845470162944*a(n-40) +13706205520330752*a(n-42) -1618885433491456*a(n-44) +103796813856768*a(n-46) -2721872609280*a(n-48).

%e Some solutions for n=2:

%e 2 3 2 3 0 1 2 1 1 1 2 3 3 3 3 3 2 1 2 1

%e 1 3 1 1 2 2 2 2 1 2 2 2 1 0 1 2 0 0 0 0

%e 0 1 0 1 3 2 1 2 0 0 1 2 0 0 0 2 3 2 1 2

%Y Column 3 of A234333.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 23 2013