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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

%I

%S 0,0,0,0,0,2,8,26,74,194,482,1152,2674,6068,13524,29704,64460,138482,

%T 294988,623834,1311086,2740666,5702270,11815752,24395678,50209572,

%U 103048168,210965064,430938832,878534170

%N 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.

%H G. C. Greubel, <a href="/A167826/b167826.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-3,0,3,2).

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

%F From _R. J. Mathar_, Feb 06 2010: (Start)

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

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

%t 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}]

%t LinearRecurrence[{4, -3, -3, 0, 3, 2}, {0, 0, 0, 0, 0, 2}, 50] (* _G. C. Greubel_, Jun 27 2016 *)

%Y Cf. A000045, A000073.

%Y Cf. A008466, A050231, A167821.

%K nonn,easy

%O 1,6

%A _V.J. Pohjola_, Nov 13 2009

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Last modified July 24 14:39 EDT 2021. Contains 346273 sequences. (Running on oeis4.)