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

Author

Alois P. Heinz, May 05 2015

Keywords

• nonn

Examples

			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.
		

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).

Crossrefs

Cf. A118430, A260697.

Programs

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 *)

Formula

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