A001603 Odd-indexed terms of A124296. (Formerly M4801 N2051)

1, 11, 101, 781, 5611, 39161, 270281, 1857451, 12744061, 87382901, 599019851, 4105974961, 28143378001, 192899171531, 1322154751061, 9062194370461, 62113232767531, 425730505493801, 2918000490238361, 20000273409331051, 137083914639998701, 939587132382262661

Offset

0,2

Comments

Old name: Related to factors of Fibonacci numbers.

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

John Cerkan, Table of n, a(n) for n = 0..1187

Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 20.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (11, -33, 33, -11, 1).

Formula

G.f.: -(1+13*x^2+x^4)/((x-1)*(x^2-3*x+1)*(x^2-7*x+1)). [After Simon Plouffe]

Maple

A001603:=-(1+13*z**2+z**4)/(z-1)/(z**2-3*z+1)/(z**2-7*z+1); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation

Mathematica

5 #^2 - 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 43, 2] (* Michael De Vlieger, Apr 03 2017 *)

Crossrefs

Cf. A001604, A124296, A124297.

Sequence in context: A156307 A057532 A193699 * A113403 A045624 A125399

Adjacent sequences: A001600 A001601 A001602 * A001604 A001605 A001606

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Entry revised by Michel Marcus and N. J. A. Sloane, Jun 06 2015

Status

approved