A298766 Number of nX4 0..1 arrays with every element equal to 1, 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

2, 52, 222, 957, 4288, 19722, 89295, 406426, 1851746, 8431005, 38382433, 174793642, 795928404, 3624236849, 16503296767, 75149172909, 342196469101, 1558217168200, 7095460966718, 32309708234520, 147124667839968, 669943229894924

Offset

1,1

Comments

Column 4 of A298770.

Links

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

Formula

Empirical: a(n) = 10*a(n-1) -38*a(n-2) +105*a(n-3) -336*a(n-4) +811*a(n-5) -1377*a(n-6) +2650*a(n-7) -3981*a(n-8) +2010*a(n-9) +1813*a(n-10) -14149*a(n-11) +47479*a(n-12) -87794*a(n-13) +154393*a(n-14) -249813*a(n-15) +293618*a(n-16) -325584*a(n-17) +254489*a(n-18) +196658*a(n-19) -968191*a(n-20) +2375306*a(n-21) -4862588*a(n-22) +7851537*a(n-23) -11495750*a(n-24) +15631765*a(n-25) -17962600*a(n-26) +18511235*a(n-27) -16755230*a(n-28) +10681320*a(n-29) -4284093*a(n-30) -3288711*a(n-31) +12217870*a(n-32) -13556672*a(n-33) +14598558*a(n-34) -17004407*a(n-35) +7774093*a(n-36) -4009403*a(n-37) +9866848*a(n-38) -3203438*a(n-39) +3961299*a(n-40) -14654649*a(n-41) +7334662*a(n-42) -1791551*a(n-43) +3980858*a(n-44) +3597567*a(n-45) -6545193*a(n-46) +2366784*a(n-47) -2366081*a(n-48) +1799656*a(n-49) +326625*a(n-50) -402654*a(n-51) -202168*a(n-52) +198284*a(n-53) -67224*a(n-54) +127183*a(n-55) +1274*a(n-56) -38064*a(n-57) -10556*a(n-58) +1228*a(n-59) -4192*a(n-60) -994*a(n-61) -56*a(n-62) -422*a(n-63) -60*a(n-64) +32*a(n-66) for n>69

Example

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

Crossrefs

Cf. A298770.

Sequence in context: A053455 A297947 A298556 * A299563 A298385 A299303

Adjacent sequences: A298763 A298764 A298765 * A298767 A298768 A298769

Keyword

nonn

Author

R. H. Hardin, Jan 26 2018

Status

approved