A260505 Number of binary words of length n with exactly one occurrence of subword 010 and exactly two occurrences of subword 101.

0, 0, 0, 0, 0, 1, 2, 7, 16, 38, 82, 175, 362, 736, 1468, 2885, 5596, 10736, 20398, 38423, 71818, 133307, 245890, 450970, 822788, 1493992, 2700800, 4862566, 8721608, 15588371, 27770338, 49320863, 87344004, 154263972, 271765362, 477622769, 837519742, 1465470968

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,10,6,-18,11,6,-10,2,3,-2,-1).

Formula

G.f.: -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4).

Example

a(5) = 1: 10101.
a(6) = 2: 101011, 110101.
a(7) = 7: 0101101, 0110101, 1010110, 1010111, 1011010, 1101011, 1110101.
a(8) = 16: 00101101, 00110101, 01011011, 01011101, 01101011, 01110101, 10101100, 10101110, 10101111, 10110100, 10111010, 11010110, 11010111, 11011010, 11101011, 11110101.
a(9) = 38: 000101101, 000110101, 001011011, ..., 111011010, 111101011, 111110101.
a(10) = 82: 0000101101, 0000110101, 0001011011, ..., 1111011010, 1111101011, 1111110101.

Maple

gf:= -x^5*(2*x^2-x+1)*(x-1)^3/((x^2-x+1)^2*(x^2+x-1)^4):
a:= n-> coeff(series(gf, x, n+1), x, n):
seq(a(n), n=0..40);

Crossrefs

Cf. A118430, A164146, A255386, A260668, A260697.

Sequence in context: A269963 A176805 A224227 * A042243 A293378 A041887

Adjacent sequences: A260502 A260503 A260504 * A260506 A260507 A260508

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 11 2015

Status

approved