A140107 a(n) = binomial(n+3, 3)*7^n.

1, 28, 490, 6860, 84035, 941192, 9882516, 98825160, 951192165, 8877793540, 80787921214, 719746934452, 6297785676455, 54257845827920, 461191689537320, 3874010192113488, 32202709721943369, 265198785945415980, 2165790085220897170, 17554298585474640220

Offset

0,2

Comments

With a different offset, number of n-permutations (n=4) of 8 objects: s, t, u, v, w, z, x, y with repetition allowed, containing exactly three u's.

uuus, uusu, usuu, suuu,

uuut, uutu, utuu, tuuu,

uuuv, uuvu, uvuu, vuuu,

uuuw, uuwu, uwuu, wuuu,

uuuz, uuzu, uzuu, zuuu,

uuux, uuxu, uxuu, xuuu,

uuuy, uuyu, uyuu, yuuu

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (28,-294,1372,-2401).

Formula

From R. J. Mathar, Jun 03 2009: (Start)

a(n) = 28*a(n-1) - 294*a(n-2) + 1372*a(n-3) - 2401*a(n-4).

G.f.: 1/(7*x-1)^4. (End)

From Amiram Eldar, Aug 28 2022: (Start)

Sum_{n>=0} 1/a(n) = 756*log(7/6) - 231/2.

Sum_{n>=0} (-1)^n/a(n) = 1344*log(8/7) - 357/2. (End)

Maple

seq(binomial(n+3, 3)*7^n, n=0..26);

Mathematica

Table[Binomial[n+3, 3]7^n, {n, 0, 20}] (* or *) LinearRecurrence[{28, -294, 1372, -2401}, {1, 28, 490, 6860}, 20] (* Harvey P. Dale, Jun 21 2016 *)

Prog

(Magma) [7^n* Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
(PARI) a(n)=binomial(n+3, 3)*7^n \\ Charles R Greathouse IV, Oct 07 2015

Crossrefs

Sequence in context: A223997 A263949 A240463 * A028170 A211677 A076172

Adjacent sequences: A140104 A140105 A140106 * A140108 A140109 A140110

Keyword

nonn,easy

Author

Zerinvary Lajos, Jun 03 2008

Status

approved