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A118892
Number of binary sequences of length n containing exactly one subsequence 0110.
2
0, 0, 0, 0, 1, 4, 12, 30, 70, 156, 339, 722, 1515, 3140, 6444, 13116, 26513, 53280, 106530, 212062, 420503, 830964, 1637055, 3216240, 6303099, 12324816, 24049953, 46841550, 91074760, 176796340, 342696000, 663363750, 1282457260, 2476394580
OFFSET
0,6
COMMENTS
Column 1 of A118890. Convolution of A059633 with itself (disregard the 0 terms).
FORMULA
G.f.=z^4/(1-2z+z^3-z^4)^2.
+(-n+4)*a(n) +2*(n-3)*a(n-1) +(-n+1)*a(n-3) +n*a(n-4)=0. - R. J. Mathar, Jul 26 2022
EXAMPLE
a(5)=4 because we have 01100,01101,00110 and 10110.
MAPLE
G:=z^4/(1-2*z+z^3-z^4)^2: Gser:=series(G, z=0, 37): seq(coeff(Gser, z, n), n=0..34);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, May 04 2006
STATUS
approved