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A129982 Fibonacci numbers sandwiched between 1's. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A127203 A227288 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

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)