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A248337
6^n - 4^n.
1
0, 2, 20, 152, 1040, 6752, 42560, 263552, 1614080, 9815552, 59417600, 358602752, 2160005120, 12993585152, 78095728640, 469111242752, 2816814940160, 16909479575552, 101491237191680, 609084862103552, 3655058928435200, 21932552593866752
OFFSET
0,2
FORMULA
G.f.: 2*x/((1-4*x)*(1-6*x)).
a(n) = 10*a(n-1) - 24*a(n-2).
a(n) = 2^n*(3^n-2^n) = A000079(n) * A001047(n) = A000400(n) - A000302(n).
a(n) = 2*A081199(n). [Bruno Berselli, Oct 05 2014]
MATHEMATICA
Table[6^n - 4^n, {n, 0, 25}] (* or *) CoefficientList[Series[(2 x) / ((1 - 4 x) (1 - 6 x)), {x, 0, 30}], x]
LinearRecurrence[{10, -24}, {0, 2}, 30] (* Harvey P. Dale, Aug 18 2024 *)
PROG
(Magma) [6^n-4^n: n in [0..30]];
(PARI) vector(20, n, 6^(n-1)-4^(n-1)) \\ Derek Orr, Oct 05 2014
CROSSREFS
Cf. sequences of the form k^n-4^n: A005060 (k=5), this sequence (k=6), A190542 (k=7), A059409 (k=8), A118004 (k=9), A248338 (k=10), A139742 (k=11).
Cf. A081199.
Sequence in context: A081159 A105489 A093302 * A270444 A093130 A043029
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 05 2014
STATUS
approved