A090244 a(0) = 1; a(1) = 2; a(n) = { a(n-1) + a(n-2) for n even, a(n-1) - a(n-2) for n odd }.

1, 2, 3, 1, 4, 3, 7, 4, 11, 7, 18, 11, 29, 18, 47, 29, 76, 47, 123, 76, 199, 123, 322, 199, 521, 322, 843, 521, 1364, 843, 2207, 1364, 3571, 2207, 5778, 3571, 9349, 5778, 15127, 9349, 24476, 15127, 39603, 24476, 64079

Offset

0,2

Comments

Variant of Fibonacci sequence.

With the exception of the number 2, all numbers which occur in this sequence occur twice. The second occurrence is always 3 places after the first, e.g., a(0) = a(3) = 1; a(7) = a(10) = 7. In addition, if we take only one occurrence of each number and sort them, we get the ascending list: 1,2,3,4,7,11, ... [see A000032 or A080023].

Links

Table of n, a(n) for n=0..44.

Formula

G.f.: (1 + 2z + 2z^2 - z^3)/(1 - z^2 - z^4). [Emeric Deutsch, Jul 25 2009]

a(2n) = A000032(n+1) = A000204(n+1); a(2n+1) = A000032(n). [R. J. Mathar, Mar 22 2010]

Maple

G := (1+2*z+2*z^2-z^3)/(1-z^2-z^4): Gser := series(G, z = 0, 53): seq(coeff(Gser, z, n), n = 0 .. 50); # Emeric Deutsch, Jul 25 2009

Crossrefs

Sequence in context: A100035 A201927 A238442 * A210976 A258263 A096180

Adjacent sequences: A090241 A090242 A090243 * A090245 A090246 A090247

Keyword

easy,nonn

Author

Felix Tubiana, Jan 23 2004

Extensions

Previous a(32)-a(34) removed by Georg Fischer, Apr 16 2020

Status

approved