A284449 Number of n X 1 0..1 arrays with the number of 1's king-move adjacent to some 0 one less than the number of 0's adjacent to some 1.

0, 0, 0, 1, 2, 6, 12, 28, 56, 119, 236, 481, 950, 1902, 3752, 7450, 14684, 29032, 57192, 112850, 222308, 438359, 863808, 1703239, 3357766, 6622471, 13061980, 25772503, 50859826, 100399602, 198235896, 391523612, 773453896, 1528361734, 3020781528, 5971996960

Offset: 0

Author

R. H. Hardin, Mar 27 2017

Keywords

• nonn

Comments

Number of binary words of length n with exactly one occurrence of subword 101 more than occurrences of subword 010. a(5) = 6: 01101, 10101, 10110, 10111, 11011, 11101. - Alois P. Heinz, Apr 23 2018

Examples

			Both solutions for n=4
..0. .0
..1. .0
..0. .1
..0. .0
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3327 (first 210 terms from R. H. Hardin)

Crossrefs

Column 1 of A284455 and of A307796.

Programs

Maple

a:= proc(n) option remember; `if`(n<6, [0$3, 1, 2, 6][n+1],
      ((n+2)*(5*n^4-98*n^3+661*n^2-1680*n+1164) *a(n-1)
       -4*(2*n^5-37*n^4+226*n^3-442*n^2-87*n+204) *a(n-2)
       -2*(3*n^4-63*n^3+376*n^2-468*n+264) *a(n-3)
       +2*(8*n^5-155*n^4+1060*n^3-3035*n^2+3738*n-1752) *a(n-4)
       -4*(5*n^5-101*n^4+750*n^3-2450*n^2+3312*n-1248) *a(n-5)
       +4*(2*n-9)*(n^4-16*n^3+85*n^2-150*n+48) *a(n-6)) /
       ((n+3)*(n^4-20*n^3+139*n^2-372*n+300)))
    end:
seq(a(n), n=0..35);  # Alois P. Heinz, Apr 23 2018

Formula

Recursion: see Maple program. - Alois P. Heinz, Apr 23 2018