

A284449


Number of n X 1 0..1 arrays with the number of 1's kingmove 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
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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^498*n^3+661*n^21680*n+1164) *a(n1)
4*(2*n^537*n^4+226*n^3442*n^287*n+204) *a(n2)
2*(3*n^463*n^3+376*n^2468*n+264) *a(n3)
+2*(8*n^5155*n^4+1060*n^33035*n^2+3738*n1752) *a(n4)
4*(5*n^5101*n^4+750*n^32450*n^2+3312*n1248) *a(n5)
+4*(2*n9)*(n^416*n^3+85*n^2150*n+48) *a(n6)) /
((n+3)*(n^420*n^3+139*n^2372*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



