A208642 Number of 7 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.

64, 610, 2552, 7548, 18888, 43284, 94320, 199299, 412962, 844943, 1714680, 3461238, 6962956, 13976742, 28016664, 56111133, 112317270, 224749641, 449637728, 899440872, 1799078160, 3598388200, 7197048672, 14394415431, 28789200714

Offset

1,1

Comments

Row 7 of A208637.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 27*a(n-2) + 50*a(n-3) - 55*a(n-4) + 36*a(n-5) - 13*a(n-6) + 2*a(n-7) for n>11.

Conjectures from Colin Barker, Jul 05 2018: (Start)

G.f.: x*(64 + 98*x - 600*x^2 + 402*x^3 + 428*x^4 - 378*x^5 - 144*x^6 + 77*x^7 + 78*x^8 - 8*x^9 - 16*x^10) / ((1 - x)^6*(1 - 2*x)).

a(n) = (51480*(-3+2^(1+n)) - 71394*n - 13145*n^2 - 1205*n^3 - 55*n^4 - n^5) / 120 for n>4.

(End)

Example

Some solutions for n=4:
..0..1..0..0....0..0..1..0....0..0..1..1....0..0..0..0....0..0..0..1
..1..0..1..1....1..0..1..0....1..0..0..0....1..1..1..0....1..1..0..1
..0..1..0..1....0..1..0..1....0..1..1..1....0..0..1..1....0..1..0..1
..1..0..1..0....1..0..1..0....0..0..0..0....1..0..0..1....1..0..1..0
..1..0..1..1....1..0..1..1....1..1..1..0....1..1..0..1....0..1..0..1
..1..0..0..0....0..1..0..1....0..0..1..1....0..1..0..0....0..1..0..0
..1..1..1..1....0..1..0..1....1..0..0..1....0..1..1..1....0..1..1..1

Crossrefs

Cf. A208637.

Sequence in context: A177757 A301796 A301969 * A301890 A302086 A229401

Adjacent sequences: A208639 A208640 A208641 * A208643 A208644 A208645

Keyword

nonn

Author

R. H. Hardin, Feb 29 2012

Status

approved