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A134171 a(n) = (9/2)*(n-1)*(n-2)*(n-3). 4
0, 0, 0, 27, 108, 270, 540, 945, 1512, 2268, 3240, 4455, 5940, 7722, 9828, 12285, 15120, 18360, 22032, 26163, 30780, 35910, 41580, 47817, 54648, 62100, 70200, 78975, 88452, 98658, 109620, 121365, 133920, 147312, 161568, 176715, 192780, 209790, 227772, 246753 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Number of n permutations (n>=3) of 4 objects u, v, z, x with repetition allowed, containing n-3=0 u's. Example: if n=3 then n-3 =zero u, a()=27 because we have vzx, vxz, zvx, zxv, xvz, xzv, vvv, zzz, xxx, vvx, vxv, xvv, xxv, xvx, vxx, vvz, vzv, zvv, zzv, zvz, vzz, xzz, zxz, zzx, xxz, xzx, zxx. A027465 formatted as a triangular array: diagonal: 27, 108, 270, 540, 945, 1512. - Zerinvary Lajos, Aug 06 2008

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

D. Zvonkine, Home Page

D. Zvonkine, Counting ramified coverings and intersection theory on Hurwitz spaces II (local structure of Hurwitz spaces and combinatorial results), Moscow Mathematical Journal, vol. 7 (2007), no. 1, 135-162.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = C(n+2,3)*3^3, n>=-2. - Zerinvary Lajos, Aug 06 2008

From Chai Wah Wu, May 29 2016: (Start)

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

G.f.: 27*x^4/(x - 1)^4. (End)

MAPLE

seq(binomial(n, n-3)*3^3, n=0..39); # Zerinvary Lajos, May 18 2008

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {0, 0, 0, 27}, 50] (* G. C. Greubel, May 29 2016 *)

PROG

(MAGMA) [(9/2)*(n-1)*(n-2)*(n-3) : n in [1..50]]; // Wesley Ivan Hurt, May 29 2016

CROSSREFS

Cf. A008585, A027465, A027468. - Zerinvary Lajos, Aug 06 2008

Sequence in context: A044278 A044659 A244634 * A129026 A042426 A042424

Adjacent sequences:  A134168 A134169 A134170 * A134172 A134173 A134174

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 30 2008

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)