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
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 03 2008
STATUS
approved