

A104005


a(n+3) = a(n+2) + 3a(n+1)  2a(n); a(0) = 1, a(1) = 1, a(2)= 3.


0



1, 1, 3, 2, 9, 3, 28, 1, 91, 38, 309, 241, 1092, 1197, 3991, 5398, 14977, 23189, 57324, 96937, 222531, 398694, 872413, 1623433, 3443284, 6568757, 13651743, 26471446, 54289161, 106400013, 216324604, 426946321, 863120107, 1711309862
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OFFSET

0,3


COMMENTS

A floretiongenerated sequence relating to Fibonacci numbers and powers of 2. The sequence results from a particular transform of the sequence A000079 (powers of 2).
Can be considered the (1,3,2)weighted tribonacci sequence with seed (1,1,3). Primes include: 2, 3, 241, 23189. Semiprimes include: 9, 38, 91, 309, 3991, 5398, 14977, 222531, 1623433, 106400013, 426946321, 863120107. Note that 96937 = 31 * 53 * 59 has 3 prime factors with equal number of digits.  Jonathan Vos Post, Feb 25 2005


LINKS

Table of n, a(n) for n=0..33.
Index entries for linear recurrences with constant coefficients, signature (1, 3, 2).


FORMULA

g.f. (x1)^2/((2x1)(x^2x1)) 4a(n)  a(n+2) = Fib(n+2)*(1)^n
(1/5) [(1)^n*Lucas(n+3) + 2^n ].  Ralf Stephan, May 20 2007


PROG

Floretion Algebra Multiplication Program, FAMP Code: 1jesforseq[ (+ .5'i + .5i' + .5'ii' + .5e)*( + .5j' + .5'kk' + .5'ki' + .5e ) ], 1vesforseq = A000079(n). Identity used: jesfor = jesrightfor + jesleftfor.


CROSSREFS

Cf. A000045.
Sequence in context: A169862 A245884 A192492 * A224578 A134562 A090639
Adjacent sequences: A104002 A104003 A104004 * A104006 A104007 A104008


KEYWORD

easy,sign


AUTHOR

Creighton Dement, Feb 24 2005


STATUS

approved



