A162942 a(n) = binomial(n + 1, 2)*7^2.

0, 49, 147, 294, 490, 735, 1029, 1372, 1764, 2205, 2695, 3234, 3822, 4459, 5145, 5880, 6664, 7497, 8379, 9310, 10290, 11319, 12397, 13524, 14700, 15925, 17199, 18522, 19894, 21315, 22785, 24304, 25872, 27489, 29155, 30870, 32634, 34447, 36309

Offset

0,2

Comments

Number of n permutations (n>=2) of 8 objects r, s, t, u, v, z, x, y with repetition allowed, containing n-2 u's.

Links

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = A027469(n+2). - R. J. Mathar, Jul 18 2009

G.f.: -49*x / (x-1)^3. - R. J. Mathar, May 02 2014

From Amiram Eldar, Sep 04 2022: (Start)

Sum_{n>=1} 1/a(n) = 2/49.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*(2*log(2)-1)/49. (End)

Example

If n=2 then n-2=zero (0) u, a(1) = 49 because we have sr, tr, vr, zr, xr, yr, rs, rt, rv, rz, rx, ry, ss, st, sv, sz, sx, sy, ts, tt, tv, tz, tx, ty, vs, vt, vv, vz, vx, vy, zs, zt, zv, zz, zx, zy, xs, xt, xv, xz, xx, xy, ys, yt, yv, yz, yx, yy. If n=3 then n-2 = one (1) u, a(2) = 147 >> ssu, stu, etc.. Tf n=4 then n-2 = two (2) u, a(2) = 294 >> ssuu, stuu, ..., txuu, etc.. If n=5 then n-2 = three (3) u, a(3) = 490 >> rsuuu, stuuu, ..., rxuuu, etc..

Mathematica

Table[Binomial[n + 1, 2]*7^2, {n, 0, 58}]

Prog

(PARI) a(n)=49*binomial(n+1, 2) \\ Charles R Greathouse IV, May 02 2014

Crossrefs

Cf. A046092, A027468, A027469, A035008, A123296, A162940.

Sequence in context: A098442 A088535 A045897 * A027469 A044381 A044762

Adjacent sequences: A162939 A162940 A162941 * A162943 A162944 A162945

Keyword

nonn,easy

Author

Zerinvary Lajos, Jul 18 2009

Status

approved