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

%I #15 Sep 04 2022 04:10:27

%S 0,49,147,294,490,735,1029,1372,1764,2205,2695,3234,3822,4459,5145,

%T 5880,6664,7497,8379,9310,10290,11319,12397,13524,14700,15925,17199,

%U 18522,19894,21315,22785,24304,25872,27489,29155,30870,32634,34447,36309

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

%C 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.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = A027469(n+2). - _R. J. Mathar_, Jul 18 2009

%F G.f.: -49*x / (x-1)^3. - _R. J. Mathar_, May 02 2014

%F From _Amiram Eldar_, Sep 04 2022: (Start)

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

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

%e 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..

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

%o (PARI) a(n)=49*binomial(n+1,2) \\ _Charles R Greathouse IV_, May 02 2014

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

%K nonn,easy

%O 0,2

%A _Zerinvary Lajos_, Jul 18 2009

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Last modified March 29 10:22 EDT 2024. Contains 371268 sequences. (Running on oeis4.)