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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. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A212140 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

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Last modified June 19 03:31 EDT 2021. Contains 345125 sequences. (Running on oeis4.)