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A391835

a(n) = (1/4) * Sum_{k=0..n} (k+2) * 2^(n-k) * binomial(2*k+2,2*n-2*k+1).

1, 3, 12, 50, 179, 661, 2390, 8476, 29909, 104519, 362672, 1251478, 4295783, 14680713, 49976442, 169541536, 573390953, 1933856347, 6505983668, 21838288442, 73152323803, 244578237373, 816308965214, 2720178349156, 9051042401725, 30074946103983, 99806282153592, 330822581617182

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OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,2,-4,-33,-8,8,32,-16).

FORMULA

G.f.: (1-x-2*x^2) / ((1-x-2*x^2)^2 - 8*x^3)^2.

a(n) = 4*a(n-1) + 2*a(n-2) - 4*a(n-3) - 33*a(n-4) - 8*a(n-5) + 8*a(n-6) + 32*a(n-7) - 16*a(n-8).

MATHEMATICA

CoefficientList[Series[(1-x-2*x^2)/((1-x-2*x^2)^2-8*x^3)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jan 03 2026 *)

LinearRecurrence[{4, 2, -4, -33, -8, 8, 32, -16}, {1, 3, 12, 50, 179, 661, 2390, 8476}, 30] (* Harvey P. Dale, Feb 01 2026 *)