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
Examples
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..
Links
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Mathematica
Table[Binomial[n + 1, 2]*7^2, {n, 0, 58}] -
PARI
a(n)=49*binomial(n+1,2) \\ Charles R Greathouse IV, May 02 2014
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)
From Elmo R. Oliveira, Dec 27 2024: (Start)
E.g.f.: 49*exp(x)*x*(2 + x)/2.
a(n) = 49*A000217(n) = 49*n*(n+1)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Comments