A263120 - OEIS

%I #4 Oct 10 2015 07:05:36

%S 36,148,522,1708,5124,15640,47602,144236,432708,1295524,3883594,

%T 11649676,34949028,104703688,313818418,940969804,2822909412,

%U 8465899188,25390861962,76159749740,228479249220,685409187320,2056136698226

%N Number of (n+3)X(2+3) 0..1 arrays with each row divisible by 15 and column not divisible by 15, read as a binary number with top and left being the most significant bits.

%C Column 2 of A263124.

%H R. H. Hardin, <a href="/A263120/b263120.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) -a(n-2) -8*a(n-3) +48*a(n-4) -168*a(n-5) +48*a(n-6) +312*a(n-7) -955*a(n-8) +2884*a(n-9) -955*a(n-10) -4832*a(n-11) +7632*a(n-12) -16032*a(n-13) +7632*a(n-14) +17568*a(n-15) +4886*a(n-16) -72248*a(n-17) +4886*a(n-18) +197200*a(n-19) -366336*a(n-20) +873744*a(n-21) -366336*a(n-22) -1155888*a(n-23) +1014058*a(n-24) -588568*a(n-25) +1014058*a(n-26) -2290528*a(n-27) +6020160*a(n-28) -17209056*a(n-29) +6020160*a(n-30) +27546528*a(n-31) -27604133*a(n-32) +27776948*a(n-33) -27604133*a(n-34) +27085688*a(n-35) -75797424*a(n-36) +221932632*a(n-37) -75797424*a(n-38) -362608200*a(n-39) +362785825*a(n-40) -363318700*a(n-41) +362785825*a(n-42) -361187200*a(n-43) +406335600*a(n-44) -541780800*a(n-45) +406335600*a(n-46)

%e Some solutions for n=4

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

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

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

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

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

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

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

%Y Cf. A263124.

%K nonn

%O 1,1

%A _R. H. Hardin_, Oct 10 2015