A129982 Fibonacci numbers sandwiched between 1's.

1, 0, 1, 1, 1, 1, 1, 2, 1, 3, 1, 5, 1, 8, 1, 13, 1, 21, 1, 34, 1, 55, 1, 89, 1, 144, 1, 233, 1, 377, 1, 610, 1, 987, 1, 1597, 1, 2584, 1, 4181, 1, 6765, 1, 10946, 1, 17711, 1, 28657, 1, 46368, 1, 75025, 1, 121393, 1, 196418, 1, 317811, 1, 514229, 1, 832040, 1, 1346269, 1

Offset

0,8

Comments

This sequence is similar to Somos-5 (A006721). - Michael Somos, Aug 15 2014

Links

Table of n, a(n) for n=0..64.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,-1).

Formula

G.f.: (1 - x^2 + x^3 - x^4 - x^5) / (1 - 2*x^2 + x^6). - Michael Somos, Aug 15 2014

a(2-n) = (-1)^(mod(n, 4) == 1) * a(n) for all n in Z. - Michael Somos, Aug 15 2014

a(2*n) = 1, a(2*n + 1) = A000045(n) for all n in Z. - Michael Somos, Aug 15 2014

a(n) = 2*a(n-2) - a(n-6) for all n in Z. - Michael Somos, Aug 15 2014

0 = a(n)*a(n+5) - a(n+1)*a(n+4) - a(n+2)*a(n+3) for all even n in Z. - Michael Somos, Aug 15 2014

0 = a(n)*a(n+5) - a(n+1)*a(n+4) + a(n+2)*a(n+3) for all odd n in Z. - Michael Somos, Aug 15 2014

Example

G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^6 + 2*x^7 + x^8 + 3*x^9 + x^10 + ...

Maple

G := 1/(1-x^2)+x^3/(1-x^2-x^4); Gser := series(G, x = 0, 70); seq(coeff(Gser, x, n), n = 0 .. 65); # Emeric Deutsch, Jul 09 2007

Mathematica

a[ n_] := If[ OddQ[n], Fibonacci[ Quotient[ n, 2]], 1]; (* Michael Somos, Aug 15 2014 *)

Prog

(PARI) {a(n) = if( n%2, fibonacci( n\2), 1)}; /* Michael Somos, Aug 15 2014 */

Crossrefs

Cf. A000045, A006721.

Sequence in context: A227288 A336752 A126132 * A052552 A147000 A147486

Adjacent sequences: A129979 A129980 A129981 * A129983 A129984 A129985

Keyword

nonn,easy

Author

Paul Curtz, Jun 14 2007

Extensions

More terms from Emeric Deutsch, Jul 09 2007

Status

approved