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A260505 Number of binary words of length n with exactly one occurrence of subword 010 and exactly two occurrences of subword 101. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 14:31 EDT 2019. Contains 328094 sequences. (Running on oeis4.)