A183778 Half the number of (n+1) X 6 binary arrays with no 2 X 2 subblock having exactly 2 ones.

32, 217, 1969, 15887, 136843, 1146964, 9764363, 82573675, 701022093, 5941108591, 50402814448, 427394109663, 3625210947353, 30744778516059, 260766196940447, 2211608594540996, 18757714441639535, 159090037814462703, 1349309620582616393, 11443973193607153699, 97060893025685775328

Offset

0,1

Links

R. H. Hardin, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (4,94,-260,-3104,6922,48854, -94118,-411428,687376, 1991983,-2792826,-5747356, 6404184,9882208,-8117120, -9774592,5218304,5062656, -1310720,-1048576).

Formula

Empirical: a(n)=4*a(n-1)+94*a(n-2)-260*a(n-3)-3104*a(n-4)+6922*a(n-5)+48854*a(n-6)-94118*a(n-7)-411428*a(n-8)+687376*a(n-9)+1991983*a(n-10)-2792826*a(n-11)-5747356*a(n-12)+6404184*a(n-13)+9882208*a(n-14)-8117120*a(n-15)-9774592*a(n-16)+5218304*a(n-17)+5062656*a(n-18)-1310720*a(n-19)-1048576*a(n-20).

The above recurrence is correct. See A183782 for bounds on the order of the recurrence. - Andrew Howroyd, Jan 09 2025

Example

Some solutions with a(1,1)=0 for 3X6
..0..0..1..0..0..0....0..0..0..1..0..1....0..0..1..0..0..0....0..0..1..0..1..0
..0..0..0..0..0..0....0..0..0..0..0..0....1..0..0..0..0..1....1..0..0..0..0..0
..0..0..1..0..1..0....1..0..1..0..0..1....0..0..0..0..1..1....1..1..0..0..0..1

Crossrefs

Column k=5 of A183782.

Sequence in context: A160538 A200787 A250354 * A146089 A250232 A070053

Adjacent sequences: A183775 A183776 A183777 * A183779 A183780 A183781

Keyword

nonn,easy

Author

R. H. Hardin, Jan 07 2011

Extensions

a(0) prepended by Andrew Howroyd, Jan 09 2025

Status

approved