A198655 Number of n X 1 0..7 arrays with values 0..7 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

0, 1, 1, 2, 3, 6, 11, 23, 47, 103, 226, 518, 1200, 2867, 6946, 17234, 43393, 111418, 290233, 768819, 2064637, 5626757, 15531220, 43432402, 122878654, 351665399, 1016952840, 2970387672, 8755225931, 26027153206, 77972236615, 235260594303

Offset

1,4

Comments

Column 1 of A198661.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 7*a(n-1) + a(n-2) - 97*a(n-3) + 105*a(n-4) + 531*a(n-5) - 757*a(n-6) - 1511*a(n-7) + 2143*a(n-8) + 2457*a(n-9) - 2689*a(n-10) - 2227*a(n-11) + 1198*a(n-12) + 840*a(n-13) for n>14.

Empirical g.f.: x^2*(1 - 6*x - 6*x^2 + 85*x^3 - 25*x^4 - 476*x^5 + 247*x^6 + 1348*x^7 - 523*x^8 - 1959*x^9 + 157*x^10 + 1157*x^11 + 309*x^12) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)*(1 - x - 5*x^2)*(1 - x - 7*x^2)). - Colin Barker, Mar 02 2018

Example

All solutions for n=5:
..0....0....0
..0....0....0
..0....1....0
..0....1....1
..0....1....1

Crossrefs

Cf. A198661.

Sequence in context: A198662 A198620 A198648 * A211694 A303586 A130131

Adjacent sequences: A198652 A198653 A198654 * A198656 A198657 A198658

Keyword

nonn

Author

R. H. Hardin, Oct 28 2011

Status

approved