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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. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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

LINKS

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

FORMULA

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

EXAMPLE

Both solutions for n=4

..0. .0

..1. .0

..0. .1

..0. .0

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

CROSSREFS

Column 1 of A284455 and of A307796.

Sequence in context: A327727 A222970 A112510 * A011949 A089820 A122746

Adjacent sequences:  A284446 A284447 A284448 * A284450 A284451 A284452

KEYWORD

nonn

AUTHOR

R. H. Hardin, Mar 27 2017

STATUS

approved

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Last modified December 3 12:16 EST 2021. Contains 349462 sequences. (Running on oeis4.)