editing

approved

Number of nX5 n X 5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s1's.

Empirical: a(n) = 6*a(n-1) -15*a(n-2) +51*a(n-3) -121*a(n-4) +266*a(n-5) -598*a(n-6) +1026*a(n-7) -1958*a(n-8) +2883*a(n-9) -4421*a(n-10) +5480*a(n-11) -5762*a(n-12) +4485*a(n-13) -1246*a(n-14) -1423*a(n-15) +3587*a(n-16) -2563*a(n-17) +1429*a(n-18) +788*a(n-19) -1333*a(n-20) +2661*a(n-21) -3283*a(n-22) +2331*a(n-23) +1215*a(n-24) -4008*a(n-25) +2878*a(n-26) +724*a(n-27) -2739*a(n-28) +1555*a(n-29) +468*a(n-30) -1080*a(n-31) +418*a(n-32) +204*a(n-33) -249*a(n-34) +54*a(n-35) +44*a(n-36) -29*a(n-37) +a(n-38) +4*a(n-39) -a(n-40).

approved

editing

editing

approved

R. H. Hardin, <a href="/A296324/b296324.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX5 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1s.

1, 15, 54, 185, 853, 3569, 14691, 62193, 261763, 1099727, 4630135, 19487541, 82011553, 345200748, 1452975794, 6115623192, 25741334468, 108348131766, 456048653285, 1919560023966, 8079646389293, 34008145665113, 143144156221751

1,2

Column 5 of A296327.

Empirical: a(n) = 6*a(n-1) -15*a(n-2) +51*a(n-3) -121*a(n-4) +266*a(n-5) -598*a(n-6) +1026*a(n-7) -1958*a(n-8) +2883*a(n-9) -4421*a(n-10) +5480*a(n-11) -5762*a(n-12) +4485*a(n-13) -1246*a(n-14) -1423*a(n-15) +3587*a(n-16) -2563*a(n-17) +1429*a(n-18) +788*a(n-19) -1333*a(n-20) +2661*a(n-21) -3283*a(n-22) +2331*a(n-23) +1215*a(n-24) -4008*a(n-25) +2878*a(n-26) +724*a(n-27) -2739*a(n-28) +1555*a(n-29) +468*a(n-30) -1080*a(n-31) +418*a(n-32) +204*a(n-33) -249*a(n-34) +54*a(n-35) +44*a(n-36) -29*a(n-37) +a(n-38) +4*a(n-39) -a(n-40)

Some solutions for n=5

..1..1..0..1..1. .0..0..1..1..0. .0..0..0..0..1. .0..1..1..1..1

..1..0..0..1..0. .0..1..0..1..0. .0..0..0..1..1. .1..0..0..0..1

..0..0..0..0..0. .1..0..1..0..0. .1..1..0..0..0. .1..0..1..1..0

..0..0..0..0..1. .1..1..0..0..0. .1..0..0..0..0. .1..1..0..0..1

..0..0..0..1..1. .0..0..0..0..0. .0..0..0..0..0. .0..0..0..1..1

Cf. A296327.

allocated

nonn

R. H. Hardin, Dec 10 2017

approved

editing

allocated for R. H. Hardin

allocated

approved