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A202442 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals. 1

%I

%S 224,376,676,1102,1722,2544,3652,5054,6850,9048,11764,15006,18906,

%T 23472,28852,35054,42242,50424,59780,70318,82234,95536,110436,126942,

%U 145282,165464,187732,212094,238810,267888,299604,333966,371266,411512,455012

%N Number of (n+2) X 5 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.

%C Column 3 of A202447.

%H R. H. Hardin, <a href="/A202442/b202442.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) -a(n-2) -5*a(n-3) +5*a(n-4) +a(n-5) -3*a(n-6) +a(n-7) for n>8.

%F Conjectures from _Colin Barker_, May 29 2018: (Start)

%F G.f.: 2*x*(112 - 148*x - 114*x^2 + 285*x^3 - 74*x^4 - 122*x^5 + 84*x^6 - 15*x^7) / ((1 - x)^5*(1 + x)^2).

%F a(n) = (n^4 + 24*n^3 + 149*n^2 + 492*n + 468) / 6 for n even.

%F a(n) = (n^4 + 24*n^3 + 149*n^2 + 498*n + 492) / 6 for n>1 and odd.

%F (End)

%e Some solutions for n=4:

%e ..1..1..1..1..1....0..1..0..1..1....1..1..1..1..1....1..1..1..1..1

%e ..0..1..0..0..0....1..1..1..1..1....1..0..0..0..0....1..0..1..0..0

%e ..0..1..1..1..1....0..1..1..1..1....1..1..1..1..1....1..0..1..1..1

%e ..0..1..0..1..1....1..1..1..1..1....1..0..1..0..1....1..0..1..1..1

%e ..0..1..0..1..1....1..1..1..1..1....1..1..1..1..1....1..0..1..1..1

%e ..0..1..0..1..1....1..1..1..1..1....1..1..1..1..1....1..0..1..1..1

%Y Cf. A202447.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 19 2011

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Last modified March 25 01:20 EDT 2023. Contains 361511 sequences. (Running on oeis4.)