OFFSET
0,2
COMMENTS
With a different offset, number of n-permutations (n >= 6) of 8 objects: r, s, t, u, v, z, x, y with repetition allowed, containing exactly six (6) u's. - Zerinvary Lajos, Jun 16 2008
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (49, -1029, 12005, -84035, 352947, -823543, 823543).
FORMULA
a(n) = 7^n*binomial(n+6, 6).
G.f.: 1/(1-7*x)^7.
a(n) = 49*a(n-1) - 1029*a(n-2) + 12005*a(n-3) - 84035*a(n-4) + 352947*a(n-5) - 823543*a(n-6) + 823543*a(n-7), a(0)=1, a(1)=49, a(2)=1372, a(3)=28812, a(4)=504210, a(5)=7764834, a(6)=108707676. - Harvey P. Dale, Feb 21 2013
MAPLE
seq(binomial(n+6, 6)*7^n, n=0..16); # Zerinvary Lajos, Jun 16 2008
MATHEMATICA
CoefficientList[Series[1/(1-7x)^7, {x, 0, 20}], x] (* or *) LinearRecurrence[ {49, -1029, 12005, -84035, 352947, -823543, 823543}, {1, 49, 1372, 28812, 504210, 7764834, 108707676}, 20] (* Harvey P. Dale, Feb 21 2013 *)
PROG
(Sage)[lucas_number2(n, 7, 0)*binomial(n, 6)/7^6 for n in range(6, 22)] # Zerinvary Lajos, Mar 13 2009
(Magma) [7^n* Binomial(n+6, 6): n in [0..20]]; // Vincenzo Librandi, Oct 12 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved