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A190543
a(n) = 8^n - 3^n.
3
0, 5, 55, 485, 4015, 32525, 261415, 2094965, 16770655, 134198045, 1073682775, 8589757445, 68718945295, 549754219565, 4398041728135, 35184357739925, 281474933663935, 2251799684545085, 18014398122061495, 144115186913594405
OFFSET
0,2
COMMENTS
Length-n words from letters {1, 2, ..., 8} with at least one letter greater than 3. - Joerg Arndt, Jun 02 2011
All terms are odd multiples of 5, since the powers of 8 mod 10 are 8, 4, 2, 6, ... and the powers of 3 mod 10 are 3, 9, 7, 1, ... - Alonso del Arte, Feb 25 2014
LINKS
Feryal Alayont and Evan Henning, Edge Covers of Caterpillars, Cycles with Pendants, and Spider Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.9.4.
FORMULA
a(n) = 11*a(n-1) - 24*a(n-2).
a(n) = A001018(n) - A000244(n). - Michel Marcus, Feb 26 2014
G.f.: 5*x/((1-3*x)*(1-8*x)). - Vincenzo Librandi, Oct 05 2014
a(n+1) = 5*A016140(n). - Vincenzo Librandi, Oct 05 2014
MAPLE
A190543:=n->8^n - 3^n; seq(A190543(n), n=0..20); # Wesley Ivan Hurt, Feb 26 2014
MATHEMATICA
Table[8^n - 3^n, {n, 0, 19}] (* Alonso del Arte, Feb 25 2014 *)
CoefficientList[Series[5 x/((1 - 3 x) (1 - 8 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)
PROG
(Magma) [8^n - 3^n: n in [0..30]]
(PARI) a(n)=8^n-3^n \\ Charles R Greathouse IV, Jun 02 2011
CROSSREFS
Sequence in context: A335355 A306095 A081300 * A144894 A247775 A045640
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jun 02 2011
STATUS
approved