A003481 a(n) = 7*a(n-1) - a(n-2) + 5.
2, 20, 143, 986, 6764, 46367, 317810, 2178308, 14930351, 102334154, 701408732, 4807526975, 32951280098, 225851433716, 1548008755919, 10610209857722, 72723460248140, 498454011879263, 3416454622906706, 23416728348467684, 160500643816367087, 1100087778366101930
Offset: 0
References
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- T. D. Noe, Table of n, a(n) for n = 0..200
- 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.
- John Riordan and N. J. A. Sloane, Correspondence, 1974.
- S. M. Tanny and M. Zuker, On a unimodal sequence of binomial coefficients, Discrete Math. 9 (1974), 79-89.
- Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
Crossrefs
Cf. A033888.
Programs
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Mathematica
t = {2, 20}; Do[AppendTo[t, 7*t[[-1]] - t[[-2]] + 5], {n, 2, 30}] (* T. D. Noe, Oct 07 2013 *) nxt[{a_,b_}]:={b,7b-a+5}; NestList[nxt,{2,20},30][[All,1]] (* Harvey P. Dale, Aug 11 2019 *)
Formula
G.f.: ( -2-4*x+x^2 ) / ( (x-1)*(x^2-7*x+1) ). - Simon Plouffe in his 1992 dissertation
a(n) = Fibonacci(4(n+1)) - 1 = A033888(n+1) - 1. - Ralf Stephan, Feb 24 2004, index corrected R. J. Mathar, Sep 18 2008
Extensions
More terms from Ralf Stephan, Feb 24 2004