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A104487
a(n+3) = 6a(n+2) - 10a(n+1) + 3a(n); a(0) = 1, a(1) = 4, a(2) = 14.
1
1, 4, 14, 47, 154, 496, 1577, 4964, 15502, 48103, 148490, 456416, 1397905, 4268740, 13002638, 39522143, 119912698, 363262672, 1099015481, 3321204260, 10026858766, 30246156439, 91171963754, 274650794432, 826923598369
OFFSET
0,2
COMMENTS
Binomial transform of A104004.
If another a(0)=0 is added in front, also the binomial transform of A027934.
FORMULA
G.f.: (2*x-1)/((3*x-1)*(x^2-3*x+1)). Define c = (3+sqrt(5))/2 and d = (3-sqrt(5))/2. Then a(n) = 3^(n+1) - ((2*sqrt(5)/5)+1)*c^n + ((2*sqrt(5)/5)-1)*d^n = 3^(n+1) - Fibonacci(2n+3). - Ralf Stephan, May 20 2007
MATHEMATICA
LinearRecurrence[{6, -10, 3}, {1, 4, 14}, 30] (* Harvey P. Dale, May 07 2017 *)
PROG
(Magma) [3^(n+1) - Fibonacci(2*n+3): n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
CROSSREFS
Sequence in context: A291385 A192877 A263622 * A247210 A094789 A273714
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Apr 19 2005
EXTENSIONS
Comment concerning the binomial transforms corrected by R. J. Mathar, Oct 26 2009
STATUS
approved