A304475 Number of nX4 0..1 arrays with every element unequal to 0, 1, 2, 4 or 6 king-move adjacent elements, with upper left element zero.

8, 24, 37, 110, 297, 869, 2325, 6379, 17568, 48401, 132571, 364655, 1002589, 2754738, 7567524, 20801769, 57166345, 157087321, 431686614, 1186366477, 3260212654, 8959296665, 24621148350, 67661598847, 185940093307, 510981495243

Offset

1,1

Comments

Column 4 of A304479.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) +7*a(n-3) +7*a(n-4) -14*a(n-5) -28*a(n-6) -56*a(n-7) -65*a(n-8) -77*a(n-9) +31*a(n-10) +280*a(n-11) +458*a(n-12) +484*a(n-13) +398*a(n-14) +320*a(n-15) -333*a(n-16) -1155*a(n-17) -1849*a(n-18) -2523*a(n-19) -2612*a(n-20) -1778*a(n-21) +445*a(n-22) +2555*a(n-23) +4684*a(n-24) +7438*a(n-25) +7323*a(n-26) +4721*a(n-27) +1048*a(n-28) -1452*a(n-29) -6069*a(n-30) -11167*a(n-31) -10559*a(n-32) -6445*a(n-33) -3475*a(n-34) -2108*a(n-35) +2357*a(n-36) +8323*a(n-37) +7696*a(n-38) +5753*a(n-39) +4296*a(n-40) +3014*a(n-41) +73*a(n-42) -2650*a(n-43) -2475*a(n-44) -2110*a(n-45) -2531*a(n-46) -2247*a(n-47) -526*a(n-48) +835*a(n-49) +429*a(n-50) -103*a(n-51) +197*a(n-52) +558*a(n-53) +517*a(n-54) +283*a(n-55) +4*a(n-56) -156*a(n-57) -91*a(n-58) +29*a(n-59) +68*a(n-60) -72*a(n-61) -100*a(n-62) -32*a(n-63) +32*a(n-64) +24*a(n-65) for n>67

Example

Some solutions for n=5
..0..1..0..0. .0..0..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0
..1..0..0..0. .1..1..1..1. .1..1..1..1. .0..1..0..0. .1..1..0..0
..0..0..0..0. .0..0..1..1. .1..1..1..0. .0..0..1..1. .1..1..1..1
..0..0..0..1. .0..0..0..0. .0..1..1..0. .0..0..0..0. .1..1..0..0
..0..0..1..0. .0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0

Crossrefs

Cf. A304479.

Sequence in context: A305241 A044450 A134223 * A316300 A050427 A329549

Adjacent sequences: A304472 A304473 A304474 * A304476 A304477 A304478

Keyword

nonn

Author

R. H. Hardin, May 13 2018

Status

approved