A104005 a(n+3) = a(n+2) + 3a(n+1) - 2a(n); a(0) = 1, a(1) = -1, a(2)= 3.

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

Offset

0,3

Comments

A floretion-generated sequence relating to Fibonacci numbers and powers of 2. The sequence results from a particular transform of the sequence A000079 (powers of 2).

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.

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. (x-1)^2/((2x-1)(x^2-x-1)) 4a(n) - a(n+2) = Fib(n+2)*(-1)^n

(1/5) [(-1)^n*Lucas(n+3) + 2^n ]. - Ralf Stephan, May 20 2007

Crossrefs

Cf. A000045.

Sequence in context: A245884 A192492 A351444 * A224578 A134562 A090639

Adjacent sequences: A104002 A104003 A104004 * A104006 A104007 A104008

Keyword

easy,sign

Author

Creighton Dement, Feb 24 2005

Status

approved