A255386 Number of binary words of length n with exactly one occurrence of subword 010 and exactly one occurrence of subword 101.

0, 0, 0, 0, 2, 4, 10, 20, 42, 84, 166, 320, 608, 1140, 2116, 3892, 7102, 12868, 23170, 41488, 73918, 131104, 231578, 407520, 714672, 1249368, 2177736, 3785688, 6564362, 11355940, 19602154, 33767228, 58056786, 99638364, 170711134, 292011872, 498747632

Offset

0,5

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,-4,-2,5,-2,-2,2,1).

Formula

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

Example

a(4) = 2: 0101, 1010.
a(5) = 4: 00101, 01011, 10100, 11010.
a(6) = 10: 000101, 001011, 010110, 010111, 011010, 100101, 101000, 101001, 110100, 111010.
a(8) = 42: 00000101, 00001011, 00010110, 00010111, 00011010, 00101100, 00101110, 00101111, 00110100, 00111010, 01001101, 01011000, 01011001, 01011100, 01011110, 01011111, 01100101, 01101000, 01101001, 01110100, 01111010, 10000101, 10001011, 10010110, 10010111, 10011010, 10100000, 10100001, 10100011, 10100110, 10100111, 10110010, 11000101, 11001011, 11010000, 11010001, 11010011, 11100101, 11101000, 11101001, 11110100, 11111010.

Maple

a:= n-> coeff(series(-2*x^4*(x-1)^2/
        ((x^2-x+1)*(x^2+x-1)^3), x, n+1), x, n):
seq(a(n), n=0..50);

Mathematica

LinearRecurrence[{4, -4, -2, 5, -2, -2, 2, 1}, {0, 0, 0, 0, 2, 4, 10, 20}, 40] (* Harvey P. Dale, Apr 09 2016 *)

Crossrefs

Cf. A118430, A260697.

Sequence in context: A283213 A283251 A318975 * A167030 A026644 A167193

Adjacent sequences: A255383 A255384 A255385 * A255387 A255388 A255389

Keyword

nonn

Author

Alois P. Heinz, May 05 2015

Status

approved