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%I #18 Mar 06 2024 15:45:29
%S 1,-1,3,-2,9,-3,28,1,91,38,309,241,1092,1197,3991,5398,14977,23189,
%T 57324,96937,222531,398694,872413,1623433,3443284,6568757,13651743,
%U 26471446,54289161,106400013,216324604,426946321,863120107,1711309862
%N a(n+3) = a(n+2) + 3a(n+1) - 2a(n); a(0) = 1, a(1) = -1, a(2)= 3.
%C 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).
%C 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.
%C 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
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 3, -2).
%F g.f. (x-1)^2/((2x-1)(x^2-x-1)) 4a(n) - a(n+2) = Fib(n+2)*(-1)^n
%F (1/5) [(-1)^n*Lucas(n+3) + 2^n ]. - _Ralf Stephan_, May 20 2007
%Y Cf. A000045.
%K easy,sign
%O 0,3
%A _Creighton Dement_, Feb 24 2005
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