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A081656
a(n) = 2*6^n - 2^n.
4
1, 10, 68, 424, 2576, 15520, 93248, 559744, 3358976, 20154880, 120931328, 725592064, 4353560576, 26121379840, 156728311808, 940369936384, 5642219749376, 33853318758400, 203119913074688, 1218719479496704, 7312316879077376, 43873901278658560, 263243407680339968
OFFSET
0,2
COMMENTS
Binomial transform of A081655.
Inverse binomial transform of A081657.
FORMULA
G.f.: (1+2*x)/((1-6*x)(1-2*x)).
E.g.f.: 2*exp(6*x) - exp(2*x).
a(0)=1, a(2)=10; for n>2, a(n) = 8*a(n-1) - 12*a(n-2). - Vincenzo Librandi, Aug 10 2013
MATHEMATICA
CoefficientList[Series[(1 + 2 x) / ((1 - 6 x) (1 - 2 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
Table[2*6^n-2^n, {n, 0, 20}] (* or *) LinearRecurrence[{8, -12}, {1, 10}, 20] (* Harvey P. Dale, Mar 17 2019 *)
PROG
(Magma) [2*6^n-2^n: n in [0..30]]; // Vincenzo Librandi, Aug 10 2013
(PARI) a(n)=2*6^n-2^n \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
Third column of array A094424.
Sequence in context: A104598 A026901 A027242 * A219466 A330352 A321060
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 26 2003
STATUS
approved