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A053602 a(n) = a(n-1)-(-1)^n*a(n-2), a(0)=0, a(1)=1. 8
0, 1, 1, 2, 1, 3, 2, 5, 3, 8, 5, 13, 8, 21, 13, 34, 21, 55, 34, 89, 55, 144, 89, 233, 144, 377, 233, 610, 377, 987, 610, 1597, 987, 2584, 1597, 4181, 2584, 6765, 4181, 10946, 6765, 17711, 10946, 28657, 17711, 46368, 28657, 75025, 46368, 121393, 75025 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

If b(0)=0, b(1)=1 and b(n)=b(n-1)+(-1)^n*b(n-2), then a(n)=b(n+3). - Jaume Oliver Lafont, Oct 03 2009

a(n) is the number of palindromic compositions of n-1 into parts of 1 and 2. a(7) = 5 because we have: 2+2+2, 2+1+1+2, 1+2+2+1, 1+1+2+1+1, 1+1+1+1+1+1. - Geoffrey Critzer, Mar 17 2014

LINKS

Table of n, a(n) for n=0..50.

Krithnaswami Alladi and V. E. Hoggatt, Jr. Compositions with Ones and Twos, Fibonacci Quarterly, 13 (1975), 233-239 - Ron Knott, Oct 29 2010

Index entries for two-way infinite sequences

Index to sequences with linear recurrences with constant coefficients, signature (0,1,0,1)

FORMULA

G.f.: x*(1+x+x^2)/(1-x^2-x^4).

a(n) = a(n-2)+a(n-4).

a(2n) = F(n), a(2n-1) = F(n+1) where F() is Fibonacci sequence.

a(3)=1, a(4)=2, a(n+2) = a(n+1)+sign(a(n)-a(n+1))*a(n), n>4. - Benoit Cloitre, Apr 08 2002

a(n) = A079977(n-1) + A079977(n-2) + A079977(n-3), n>2. - Ralf Stephan, Apr 26 2003

a(0) = 0, a(1) = 1; a(2n) = a(2n-1)-a(2n-2); a(2n+1) = a(2n) + a(2n-1). - Amarnath Murthy, Jul 21 2005

MATHEMATICA

nn=50; CoefficientList[Series[x (1+x+x^2)/(1-x^2-x^4), {x, 0, nn}], x] (* Geoffrey Critzer, Mar 17 2014 *)

PROG

(PARI) a(n)=fibonacci(n\2+n%2*2)

CROSSREFS

a(3-n) = A051792(n). Cf. A000045.

Sequence in context: A132091 A239881 A051792 * A123231 A246995 A238782

Adjacent sequences:  A053599 A053600 A053601 * A053603 A053604 A053605

KEYWORD

nonn,easy

AUTHOR

Michael Somos, Jan 17 2000

STATUS

approved

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Last modified October 1 00:26 EDT 2014. Contains 247498 sequences.