A001603 Odd-indexed terms of A124296.
1, 11, 101, 781, 5611, 39161, 270281, 1857451, 12744061, 87382901, 599019851, 4105974961, 28143378001, 192899171531, 1322154751061, 9062194370461, 62113232767531, 425730505493801, 2918000490238361, 20000273409331051, 137083914639998701, 939587132382262661
Offset: 0
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).
Programs
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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
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Mathematica
5 #^2 - 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 43, 2] (* Michael De Vlieger, Apr 03 2017 *)
Formula
G.f.: -(1+13*x^2+x^4)/((x-1)*(x^2-3*x+1)*(x^2-7*x+1)). [After Simon Plouffe]
Extensions
Entry revised by Michel Marcus and N. J. A. Sloane, Jun 06 2015
Comments