A167826 a(n) is the number of n-tosses having a run of 3 or more heads and a run of 3 or more tails for a fair coin.

0, 0, 0, 0, 0, 2, 8, 26, 74, 194, 482, 1152, 2674, 6068, 13524, 29704, 64460, 138482, 294988, 623834, 1311086, 2740666, 5702270, 11815752, 24395678, 50209572, 103048168, 210965064, 430938832, 878534170

Offset

1,6

Links

G. C. Greubel, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (4,-3,-3,0,3,2).

Formula

a(n) = 2^n - 2*(tribonacci(n+3) - Fibonacci(n+1)), where tribonacci = A000073.

From R. J. Mathar, Feb 06 2010: (Start)

a(n) = 4*a(n-1) - 3*a(n-2) - 3*a(n-3) + 3*a(n-5) + 2*a(n-6).

G.f.: -2*x^6/((2*x-1)*(x^2+x-1)*(x^3+x^2+x-1)). (End)

Mathematica

b[1] = 0; b[2] = 1; b[3] = 1; b[n_]: = b[n-1] + b[n-2] + b[n-3]; Table[2^n - 2*(Sum[b[n + 3 - i], {i, 1, 3}] - Fibonacci[n + 1]), {n, 1, 30}]
LinearRecurrence[{4, -3, -3, 0, 3, 2}, {0, 0, 0, 0, 0, 2}, 50] (* G. C. Greubel, Jun 27 2016 *)

Crossrefs

Cf. A000045, A000073.

Cf. A008466, A050231, A167821.

Sequence in context: A357283 A136594 A268502 * A301995 A325926 A097040

Adjacent sequences: A167823 A167824 A167825 * A167827 A167828 A167829

Keyword

nonn,easy

Author

V.J. Pohjola, Nov 13 2009

Status

approved