A234551 - OEIS

A234551

Number of (n+1) X (2+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).

%I #6 Jun 20 2022 18:25:12

%S 2716,22458,184816,1527660,12632704,104793676,870061872,7247511972,

%T 60427123392,505598378732,4234359329552,35597000634596,

%U 299528022187872,2530562921714700,21397823598521904,181712718030164164

%N Number of (n+1) X (2+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 3 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234551/b234551.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 25*a(n-1) +171*a(n-2) -8947*a(n-3) +20442*a(n-4) +1276046*a(n-5) -7721142*a(n-6) -89665378*a(n-7) +835291375*a(n-8) +2916848953*a(n-9) -45270570765*a(n-10) -12096348459*a(n-11) +1332333947744*a(n-12) -1813960758728*a(n-13) -21440506572936*a(n-14) +48154351857440*a(n-15) +200413362270168*a(n-16) -574094316035800*a(n-17) -1131202886847072*a(n-18) +3914657325465440*a(n-19) +3861853479350272*a(n-20) -16494937667180864*a(n-21) -7509328290739200*a(n-22) +44239728068980992*a(n-23) +6116716146439680*a(n-24) -75931240737844224*a(n-25) +4864198828197888*a(n-26) +81940531841003520*a(n-27) -16357767821991936*a(n-28) -52834812420096000*a(n-29) +15489875939328000*a(n-30) +18143005999104000*a(n-31) -6490659697459200*a(n-32) -2459495301120000*a(n-33) +983798120448000*a(n-34).

%e Some solutions for n=3:

%e 2 3 1 0 5 1 0 5 2 0 1 6 3 3 6 4 4 2 3 6 0

%e 1 5 6 3 5 4 2 4 4 0 4 6 6 3 3 4 1 2 0 6 3

%e 3 4 2 2 1 3 2 1 4 3 4 3 4 4 1 4 4 2 3 6 6

%e 4 2 3 5 1 0 0 2 2 1 5 1 4 1 1 5 2 3 0 0 3

%Y Column 2 of A234555.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 28 2013