A299524 Number of nX4 0..1 arrays with every element equal to 1, 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 16, 12, 166, 537, 2573, 16538, 83533, 420801, 2412733, 12975515, 68321766, 376287484, 2042163601, 10949762356, 59563103680, 323175890698, 1744473182106, 9456860848043, 51262356984369, 277339276333524, 1502217683264205

Offset

1,2

Comments

Column 4 of A299528.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) +6*a(n-2) +85*a(n-3) -308*a(n-4) -556*a(n-5) -2039*a(n-6) +8843*a(n-7) +12024*a(n-8) +17861*a(n-9) -101643*a(n-10) -117910*a(n-11) +20768*a(n-12) +467084*a(n-13) +219710*a(n-14) -596837*a(n-15) -274594*a(n-16) +2569583*a(n-17) +862440*a(n-18) -8787502*a(n-19) -6703808*a(n-20) +11888135*a(n-21) +14350201*a(n-22) -10727892*a(n-23) -4048480*a(n-24) +17735232*a(n-25) +378931*a(n-26) -61474291*a(n-27) -1822713*a(n-28) +69458328*a(n-29) +64624442*a(n-30) -100064304*a(n-31) -92228173*a(n-32) +93263599*a(n-33) +111255163*a(n-34) -34509077*a(n-35) -139754553*a(n-36) +20038295*a(n-37) +75556687*a(n-38) -8174840*a(n-39) -19932098*a(n-40) +9495345*a(n-41) +786307*a(n-42) -6111053*a(n-43) -70336*a(n-44) +1689102*a(n-45) +210409*a(n-46) -72486*a(n-47) -14748*a(n-48) -16400*a(n-49) -1098*a(n-50) +36*a(n-51) -40*a(n-52) +40*a(n-53) for n>56

Example

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

Crossrefs

Cf. A299528.

Sequence in context: A070551 A028493 A291426 * A070534 A269299 A070577

Adjacent sequences: A299521 A299522 A299523 * A299525 A299526 A299527

Keyword

nonn

Author

R. H. Hardin, Feb 11 2018

Status

approved