|
|
COMMENTS
|
With a different offset, number of n-permutations (n>=7) of 7 objects: s, t, u, v, z, x, y with repetition allowed, containing exactly seven (7) u's.
If n=7 then a(0)= 1 because we have uuuuuuu
a(1)=48 because we have
uuuuuuus, uuuuuuut, uuuuuuuv, uuuuuuuz, uuuuuuux, uuuuuuuy,
uuuuuusu, uuuuuutu, uuuuuuvu, uuuuuuzu, uuuuuuxu, uuuuuuyu,
uuuuusuu, uuuuutuu, uuuuuvuu, uuuuuzuu, uuuuuxuu, uuuuuyuu,
uuuusuuu, uuuutuuu, uuuuvuuu, uuuuzuuu, uuuuxuuu, uuuuyuuu,
uuusuuuu, uuutuuuu, uuuvuuuu, uuuzuuuu, uuuxuuuu, uuuyuuuu,
uusuuuuu, uutuuuuu, uuvuuuuu, uuzuuuuu, uuxuuuuu, uuyuuuuu,
usuuuuuu, utuuuuuu, uvuuuuuu, uzuuuuuu, uxuuuuuu, uyuuuuuu,
suuuuuuu, tuuuuuuu, vuuuuuuu, zuuuuuuu, xuuuuuuu, yuuuuuuu.
|
|
|
PROG
|
(Sage)[lucas_number2(n, 6, 0)*binomial(n, 7)/6^7for n in range(7, 24)] # Zerinvary Lajos, Mar 13 2009
(MAGMA) [6^n* Binomial(n+7, 7): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
(PARI) vector(15, n, binomial(n+6, 7)*6^(n-1)) \\ Derek Orr, Jul 24 2017
|
