|
| |
|
|
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 }.
|
|
0
| |
|
|
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, 843, 2207, 1364, 3571, 2207, 5778, 3571, 9349, 5778, 15127, 9349, 24476, 15127, 39603, 24476, 64079, 39603, 103682, 64079
(list; graph; refs; listen; history; internal format)
|
|
|
|
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, i.e. 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].
|
|
|
FORMULA
| Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 25 2009: (Start)
G.f.: G=(1+2z+2z^2-z^3)/(1-z^2-z^4).
(End)
a(2n)= A000032(n+1) = A000204(n+1). a(2n+1)=A000032(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 25 2009]
|
|
|
CROSSREFS
| Sequence in context: A140757 A100035 A201927 * A096180 A034867 A193790
Adjacent sequences: A090241 A090242 A090243 * A090245 A090246 A090247
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Felix Tubiana (fat2(AT)columbia.edu), Jan 23 2004
|
| |
|
|
