A299310 Number of nX4 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

2, 13, 29, 112, 504, 2528, 11252, 50720, 241309, 1120649, 5164117, 24001749, 111611790, 517587900, 2401369229, 11150079663, 51754367711, 240183038282, 1114814806501, 5174545144732, 24016953668166, 111472218446769

Offset

1,1

Comments

Column 4 of A299314.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) -9*a(n-2) +24*a(n-3) -47*a(n-4) -33*a(n-5) +67*a(n-6) -44*a(n-7) -1266*a(n-8) +1618*a(n-9) -650*a(n-10) +8875*a(n-11) -21535*a(n-12) +45298*a(n-13) -28362*a(n-14) +8063*a(n-15) -33255*a(n-16) +137036*a(n-17) -475039*a(n-18) +685036*a(n-19) -1381737*a(n-20) +2122260*a(n-21) -2994250*a(n-22) +3090285*a(n-23) -1926929*a(n-24) +3223180*a(n-25) -4173823*a(n-26) +4989813*a(n-27) +3861224*a(n-28) -12392223*a(n-29) +10955676*a(n-30) -4368770*a(n-31) +6543615*a(n-32) -28383782*a(n-33) +21197884*a(n-34) -9458914*a(n-35) -3445614*a(n-36) -34122171*a(n-37) +61493313*a(n-38) -7568366*a(n-39) -21654985*a(n-40) +47622275*a(n-41) -5153772*a(n-42) +1833710*a(n-43) -29408089*a(n-44) +26364129*a(n-45) -23403481*a(n-46) -25753860*a(n-47) -1475594*a(n-48) +28400558*a(n-49) -453526*a(n-50) -4211936*a(n-51) -3649669*a(n-52) -41937*a(n-53) +2293068*a(n-54) +1341106*a(n-55) +369512*a(n-56) -276982*a(n-57) -141152*a(n-58) -41792*a(n-59) -9252*a(n-60) +336*a(n-61) +148*a(n-62) for n>66

Example

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

Crossrefs

Cf. A299314.

Sequence in context: A361836 A298392 A299510 * A300111 A030452 A132602

Adjacent sequences: A299307 A299308 A299309 * A299311 A299312 A299313

Keyword

nonn

Author

R. H. Hardin, Feb 06 2018

Status

approved