login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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).

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

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 18 14:12 EST 2017. Contains 294892 sequences.