A235194 - OEIS

A235194

Number of (n+1) X (4+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%I #10 Jun 19 2022 03:33:56

%S 7072,15604,35868,96848,261760,774140,2263256,7020392,21497244,

%T 68985912,218669280,722516636,2358872824,8004360008,26827441196,

%U 93250959800,319805488320,1135256499660,3969864602232,14343676192424,50961119662300

%N Number of (n+1) X (4+1) 0..6 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 5, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).

%H R. H. Hardin, <a href="/A235194/b235194.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) +57*a(n-2) -731*a(n-3) -878*a(n-4) +26304*a(n-5) -15900*a(n-6) -552844*a(n-7) +899723*a(n-8) +7521105*a(n-9) -18125633*a(n-10) -69122561*a(n-11) +220983779*a(n-12) +431291855*a(n-13) -1831340243*a(n-14) -1746606119*a(n-15) +10803108780*a(n-16) +3716404250*a(n-17) -46315168788*a(n-18) +2550194940*a(n-19) +145490417695*a(n-20) -46954531755*a(n-21) -335197745077*a(n-22) +166429786799*a(n-23) +564880422518*a(n-24) -334400168840*a(n-25) -694120308016*a(n-26) +424547635156*a(n-27) +620744392928*a(n-28) -343613520080*a(n-29) -401608244880*a(n-30) +170947437904*a(n-31) +182786646240*a(n-32) -46865973504*a(n-33) -54609655680*a(n-34) +4665398976*a(n-35) +9369063936*a(n-36) +551978496*a(n-37) -679311360*a(n-38) -113218560*a(n-39).

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 4 of A235198.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 04 2014