OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n>=3) of 9 objects: r, s, t, u, v, w, z, x, y with repetition allowed, containing exactly (3) three u's.
Example:
(n=4) a(1)=32
uuur, uuru, uruu, ruuu,
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 (32,-384,2048,-4096).
FORMULA
G.f.: 1/(1-8*x)^4. - Vincenzo Librandi, Oct 16 2011
With offset = 3, e.g.f.: exp(8x)*x^3/3!. - Geoffrey Critzer, Oct 03 2013
From Amiram Eldar, Aug 28 2022: (Start)
Sum_{n>=0} 1/a(n) = 1176*log(8/7) - 156.
Sum_{n>=0} (-1)^n/a(n) = 1944*log(9/8) - 228. (End)
MAPLE
seq(binomial(n+3, 3)*8^n, n=0..19);
MATHEMATICA
nn = 21; Drop[Range[0, nn]!CoefficientList[Series[x^3/3! Exp[8x], {x, 0, nn}], x], 3] (* Geoffrey Critzer, Oct 03 2013 *)
PROG
(Magma) [8^n* Binomial(n+3, 3): n in [0..20]]; // Vincenzo Librandi, Oct 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jul 15 2008
STATUS
approved