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A140107 a(n) = binomial(n+3, 3)*7^n. 7
1, 28, 490, 6860, 84035, 941192, 9882516, 98825160, 951192165, 8877793540, 80787921214, 719746934452, 6297785676455, 54257845827920, 461191689537320, 3874010192113488, 32202709721943369, 265198785945415980, 2165790085220897170, 17554298585474640220 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 03 2008
STATUS
approved

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Last modified July 12 19:36 EDT 2024. Contains 374252 sequences. (Running on oeis4.)