A302214 Number of 4 X n 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

8, 3, 47, 7, 111, 80, 424, 1157, 2922, 12816, 33744, 135689, 427777, 1511455, 5237154, 17740921, 62498339, 212645123, 742064542, 2553096441, 8837428284, 30568037684, 105553660977, 365371090457, 1262061403870, 4365797662037, 15090331846613

Offset

1,1

Comments

Row 4 of A302212.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +28*a(n-2) -75*a(n-3) -398*a(n-4) +944*a(n-5) +3671*a(n-6) -7801*a(n-7) -24404*a(n-8) +47157*a(n-9) +124314*a(n-10) -221250*a(n-11) -505072*a(n-12) +836021*a(n-13) +1682425*a(n-14) -2608659*a(n-15) -4685786*a(n-16) +6844286*a(n-17) +11070045*a(n-18) -15306994*a(n-19) -22430872*a(n-20) +29493917*a(n-21) +39338431*a(n-22) -49375246*a(n-23) -60198503*a(n-24) +72293436*a(n-25) +81026935*a(n-26) -93046725*a(n-27) -96757097*a(n-28) +105632449*a(n-29) +103479364*a(n-30) -105909396*a(n-31) -100071471*a(n-32) +93611720*a(n-33) +88175650*a(n-34) -72499336*a(n-35) -70968961*a(n-36) +48606972*a(n-37) +51927035*a(n-38) -27622887*a(n-39) -34122752*a(n-40) +12814022*a(n-41) +19781216*a(n-42) -4480833*a(n-43) -9897585*a(n-44) +908537*a(n-45) +4168950*a(n-46) +107884*a(n-47) -1437073*a(n-48) -181920*a(n-49) +392409*a(n-50) +83213*a(n-51) -81617*a(n-52) -23241*a(n-53) +12292*a(n-54) +4271*a(n-55) -1246*a(n-56) -502*a(n-57) +75*a(n-58) +34*a(n-59) -2*a(n-60) -a(n-61) for n>62.

Example

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

Crossrefs

Cf. A302212.

Sequence in context: A004734 A287645 A182054 * A049074 A286034 A256046

Adjacent sequences: A302211 A302212 A302213 * A302215 A302216 A302217

Keyword

nonn

Author

R. H. Hardin, Apr 03 2018

Status

approved