The On-Line Encyclopedia of Integer Sequences (OEIS)

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A204060

G.f.: Sum_{n>=1} Fibonacci(n^2)*x^(n^2).
(history; published version)

#12 by Bruno Berselli at Mon Dec 31 03:05:02 EST 2012

STATUS

proposed

approved

#11 by Michel Marcus at Mon Dec 31 02:52:35 EST 2012

STATUS

editing

proposed

#10 by Michel Marcus at Mon Dec 31 02:51:37 EST 2012

COMMENTS

Compare g.f. to the Lambert series identity: Sum_{n>=1} lamdalambda(n)*x^n/(1-x^n) = Sum_{n>=1} x^(n^2).

STATUS

approved

editing

#9 by Paul D. Hanna at Sat Apr 07 22:52:18 EDT 2012

STATUS

editing

approved

#8 by Paul D. Hanna at Sat Apr 07 22:52:11 EDT 2012

NAME

G.f.: Sum_{n>=1} fibonacciFibonacci(n^2)*x^(n^2).

FORMULA

G.f.: Sum_{n>=1} lambda(n)*fibonacciFibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)), where lambda(n) = A008836(n) and Lucas(n) = A000204(n).

CROSSREFS

Cf. A209614 (variant).

STATUS

approved

editing

#7 by Russ Cox at Fri Mar 30 18:37:34 EDT 2012

AUTHOR

_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jan 12 2012

Discussion

Fri Mar 30

18:37

OEIS Server: https://oeis.org/edit/global/213

#6 by N. J. A. Sloane at Thu Jan 12 09:30:29 EST 2012

STATUS

proposed

approved

#5 by Paul D. Hanna at Thu Jan 12 01:43:53 EST 2012

STATUS

editing

proposed

#4 by Paul D. Hanna at Thu Jan 12 01:43:47 EST 2012

NAME

G.f.: Sum_{n>=1} fibonacci(n^2)*x^(n^2).

DATA

1, 0, 0, 3, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 0, 987, 0, 0, 0, 0, 0, 0, 0, 0, 75025, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14930352, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7778742049, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10610209857723, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37889062373143906, 0, 0, 0, 0, 0

COMMENTS

Compare g.f. to the Lambert series identity: Sum_{n>=1} lamda(n)*x^n/(1-x^n) = Sum_{n>=1} x^(n^2).

FORMULA

G.f.: Sum_{n>=1} lambda(n)*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)), where lambda(n) = A008836(n) and Lucas(n) = A000204(n).

EXAMPLE

G.f.: A(x) = x + 3*x^4 + 34*x^9 + 987*x^16 + 75025*x^25 + 14930352*x^36 +...

PROG

(PARI) {a(n)=issquare(n)*fibonacci(n)}

CROSSREFS

Cf. A203847, A054783, A008836 (lambda), A000204 (Lucas), A000045.

STATUS

proposed

editing

#3 by Paul D. Hanna at Thu Jan 12 01:30:00 EST 2012

STATUS

editing

proposed