A234186 - OEIS

A234186

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 2 (constant-stress 1 X 1 tilings).

%I #6 Jun 19 2022 01:55:17

%S 3710,44826,549448,6788640,83845322,1039633348,12874230598,

%T 160028488122,1986351882576,24751815034582,307960587879042,

%U 3847220085760804,47982564103428062,600977948816485342,7513780713855509152

%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 2 (constant-stress 1 X 1 tilings).

%H R. H. Hardin, <a href="/A234186/b234186.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 35*a(n-1) +77*a(n-2) -15290*a(n-3) +107332*a(n-4) +2296310*a(n-5) -27496928*a(n-6) -129857668*a(n-7) +2709179565*a(n-8) +391078819*a(n-9) -135239185825*a(n-10) +266375054090*a(n-11) +3713789361020*a(n-12) -12460625596968*a(n-13) -56580508651576*a(n-14) +270946287990468*a(n-15) +430387300568260*a(n-16) -3285582832195460*a(n-17) -625640021406580*a(n-18) +23032403778290512*a(n-19) -13906330678694208*a(n-20) -92444778106408560*a(n-21) +104815576682548656*a(n-22) +206598724089786048*a(n-23) -335917036867402368*a(n-24) -235981789165139328*a(n-25) +576403492940640000*a(n-26) +84728859623294976*a(n-27) -554012779297904640*a(n-28) +82836671758755840*a(n-29) +287793157283389440*a(n-30) -93776254720819200*a(n-31) -69280227459072000*a(n-32) +30100904460288000*a(n-33) +4361304342528000*a(n-34) -2076811591680000*a(n-35).

%e Some solutions for n=2:

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

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

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

%Y Column 2 of A234190.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 20 2013