OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n=5) of 8 objects s, t, u, v, w, z, x, y with repetition allowed, containing exactly four (4) u's. Example: a(1)=35 because we have
uuuus, uuusu, uusuu, usuuu, suuuu,
uuuut, uuutu, uutuu, utuuu, tuuuu,
uuuuv, uuuvu, uuvuu, uvuuu, vuuuu,
uuuuw, uuuwu, uuwuu, uwuuu, wuuuu,
uuuuz, uuuzu, uuzuu, uzuuu, zuuuu,
uuuux, uuuxu, uuxuu, uxuuu, xuuuu,
uuuuy, uuuyu, uuyuu, uyuuu, yuuuu.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (35,-490,3430,-12005,16807).
FORMULA
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 2800/3 - 6048*log(7/6).
Sum_{n>=0} (-1)^n/a(n) = 14336*log(8/7) - 5740/3. (End)
MAPLE
seq(binomial(n+4, 4)*7^n, n=0..20);
MATHEMATICA
Table[7^n * Binomial[n+4, 4], {n, 0, 20}] (* Amiram Eldar, Aug 28 2022 *)
PROG
(Magma) [7^n* Binomial(n+4, 4): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jun 12 2008
STATUS
approved