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A161727
a(n) = ((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12).
1
1, 6, 35, 202, 1161, 6662, 38203, 219018, 1255505, 7196806, 41252883, 236464586, 1355429209, 7769394054, 44534572715, 255274459018, 1463246226849, 8387401847558, 48077013831427, 275579886633162, 1579637913256745
OFFSET
0,2
COMMENTS
Fourth binomial transform of A038754, binomial transform of A140766.
FORMULA
a(n) = 8*a(n-1)-13(n-2) for n > 1; a(0) = 1, a(1) = 6.
G.f.: (1-2*x)/(1-8*x+13*x^2). - Klaus Brockhaus, Jun 19 2009
a(n) = A153594(n+1)-2*A153594(n). - R. J. Mathar, Feb 04 2021
MAPLE
seq(expand(((2+sqrt(3))*(4+sqrt(3))^n-(2-sqrt(3))*(4-sqrt(3))^n)/sqrt(12)), n = 0 .. 20) # Emeric Deutsch, Jun 20 2009
MATHEMATICA
LinearRecurrence[{8, -13}, {1, 6}, 30] (* Harvey P. Dale, Jun 01 2016 *)
PROG
(PARI) F=nfinit(x^2-3); for(n=0, 20, print1(nfeltdiv(F, ((2+x)*(4+x)^n-(2-x)*(4-x)^n), (2*x))[1], ", ")) \\ Klaus Brockhaus, Jun 19 2009
CROSSREFS
Sequence in context: A081105 A079027 A289784 * A121838 A242629 A001109
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jun 17 2009
EXTENSIONS
Extended beyond a(6) by Klaus Brockhaus and Emeric Deutsch, Jun 19 2009
Edited by Klaus Brockhaus, Jul 05 2009
STATUS
approved