A297723 Number of 4Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 4 neighboring 1s.

1, 87, 747, 4212, 36981, 336653, 2699832, 21850022, 183192407, 1522306495, 12548589707, 103837294832, 860631234338, 7123554860826, 58949780986136, 488030041372421, 4040237224677767, 33443991440492758, 276846422291175139

Offset

1,2

Comments

Row 4 of A297720.

Links

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

Formula

Empirical: a(n) = 11*a(n-1) -19*a(n-2) -10*a(n-3) +7*a(n-4) -2556*a(n-5) +9081*a(n-6) +13966*a(n-7) -77241*a(n-8) +72676*a(n-9) +28893*a(n-10) -637255*a(n-11) +1526569*a(n-12) +469389*a(n-13) -3665334*a(n-14) +4814180*a(n-15) -5319769*a(n-16) -8880003*a(n-17) +13767152*a(n-18) +6401349*a(n-19) +14938145*a(n-20) -2934050*a(n-21) -5974311*a(n-22) -80176725*a(n-23) -18087512*a(n-24) +57587221*a(n-25) +39523568*a(n-26) +107797498*a(n-27) -6507215*a(n-28) -30852088*a(n-29) -148569080*a(n-30) -36275312*a(n-31) -27497527*a(n-32) +46067911*a(n-33) +95391349*a(n-34) +24957677*a(n-35) +37407764*a(n-36) -45574161*a(n-37) -8302242*a(n-38) -34381868*a(n-39) +1027606*a(n-40) +1516924*a(n-41) +8588219*a(n-42) +4320054*a(n-43) -9970*a(n-44) -1077284*a(n-45) -1039524*a(n-46) +154880*a(n-47) +6968*a(n-48) +88752*a(n-49) +11840*a(n-50) -11008*a(n-51)

Example

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

Crossrefs

Cf. A297720.

Sequence in context: A297509 A259510 A109601 * A061625 A220055 A281806

Adjacent sequences: A297720 A297721 A297722 * A297724 A297725 A297726

Keyword

nonn

Author

R. H. Hardin, Jan 04 2018

Status

approved