A113335 -id:A113335 - cp's OEIS frontend

A102741 a(n) = 3^4 * binomial(n+3, 4).

81, 405, 1215, 2835, 5670, 10206, 17010, 26730, 40095, 57915, 81081, 110565, 147420, 192780, 247860, 313956, 392445, 484785, 592515, 717255, 860706, 1024650, 1210950, 1421550, 1658475, 1923831, 2219805, 2548665, 2912760, 3314520, 3756456, 4241160, 4771305, 5349645

Offset: 1

Zerinvary Lajos, Aug 06 2008

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A027465.

Sequences of the form 3^m*binomial(n+m-1, m): A008585 (m=1), A027468 (m=2), A134171 (m=3), this sequence (m=4), A113335 (m=5).

[3^4*Binomial(n+3,4): n in [1..30]]; // G. C. Greubel, May 17 2021

Maple
```
seq(binomial(n+3,4)*3^4, n=1..27);
```

With[{c=3^4},Table[c Binomial[n+3,4],{n,40}]]  (* Harvey P. Dale, Mar 12 2011 *)

[3^4*binomial(n+3,4) for n in (1..30)] # G. C. Greubel, May 17 2021

G.f.: 81*x/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
E.g.f.: (27/8)*x*(24 + 36*x + 12*x^2 + x^3)*exp(x). - G. C. Greubel, May 17 2021
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=1} 1/a(n) = 4/243.
Sum_{n>=1} (-1)^(n+1)/a(n) = 32*log(2)/81 - 64/243. (End)

A134171 a(n) = (9/2)(n-1)(n-2)*(n-3).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Jan 30 2008

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

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, No. 1 (2007), 135-162.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

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

Cf. A000292, A102741, A113335.

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

seq(27*binomial(n-1, 3), n=1..30); # Zerinvary Lajos, May 18 2008

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

a(n) = 27 * binomial(n-1,3). - 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/(1-x)^4. (End)
E.g.f.: 27 + (9/2*(x^3-3*x^2+6*x-6))*exp(x). - G. C. Greubel, May 17 2021
a(n) = 27 * A000292(n-3) for n >= 3. - Alois P. Heinz, May 17 2021
From Amiram Eldar, Sep 24 2022: (Start)
Sum_{n>=4} 1/a(n) = 1/18.
Sum_{n>=4} (-1)^n/a(n) = 4*log(2)/9 - 5/18. (End)

cp's OEIS Frontend

A102741 a(n) = 3^4 * binomial(n+3, 4).

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A134171 a(n) = (9/2)(n-1)(n-2)*(n-3).

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cp's OEIS Frontend

A102741 a(n) = 3^4 * binomial(n+3, 4).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Sage

Formula

A134171 a(n) = (9/2)*(n-1)*(n-2)*(n-3).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

A134171 a(n) = (9/2)(n-1)(n-2)*(n-3).