

A110211


a(n+3) = 6*a(n)  5*a(n+2), a(0) = 1, a(1) = 3, a(2) = 15.


3



1, 3, 15, 69, 327, 1545, 7311, 34593, 163695, 774609, 3665487, 17345265, 82078671, 388400433, 1837930575, 8697180849, 41155501647, 194749924785, 921566538831, 4360899684273, 20635998872655, 97650595130289, 462087577545807, 2186621894493105
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..23.
Index entries for linear recurrences with constant coefficients, signature (5, 0, 6).


FORMULA

G.f. (1+2*x)/((x1)*(6*x^2+6*x+1))
a(n)=(93*Sqrt[3]+(3Sqrt[3])^n*(4+Sqrt[3])+(3+Sqrt[3])^n*(5+2*Sqrt[3]))/(13*(3+Sqrt[3])) [From Harvey P. Dale, Mar 28 2012]


MAPLE

seriestolist(series((1+2*x)/((x1)*(6*x^2+6*x+1)), x=0, 25)); or Floretion Algebra Multiplication Program, FAMP Code: 1kbasesumseq[A*B] with A = + 'i + 'ii' + 'ij' + 'ik' and B = + .5'i  .5'j + .5'k + .5i' + .5j'  .5k'  .5'ij'  .5'ik' + .5'ji' + .5'ki' Sumtype is set to: sum[(Y[0], Y[1], Y[2]), mod(3)


MATHEMATICA

LinearRecurrence[{5, 0, 6}, {1, 3, 15}, 30] (* Harvey P. Dale, Mar 28 2012 *)


CROSSREFS

Cf. A110210, A110212, A110213.
Sequence in context: A213451 A224749 A122558 * A167874 A318967 A277370
Adjacent sequences: A110208 A110209 A110210 * A110212 A110213 A110214


KEYWORD

easy,sign


AUTHOR

Creighton Dement, Jul 16 2005


STATUS

approved



