A000383 Hexanacci numbers with a(0) = ... = a(5) = 1.
1, 1, 1, 1, 1, 1, 6, 11, 21, 41, 81, 161, 321, 636, 1261, 2501, 4961, 9841, 19521, 38721, 76806, 152351, 302201, 599441, 1189041, 2358561, 4678401, 9279996, 18407641, 36513081, 72426721, 143664401, 284970241, 565262081, 1121244166, 2224080691, 4411648301
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
- Indranil Ghosh, Table of n, a(n) for n = 0..3358 (terms 0..200 from T. D. Noe)
- Joerg Arndt, Matters Computational (The Fxtbook)
- B. G. Baumgart, Letter to the editor Part 1 Part 2 Part 3, Fib. Quart. 2 (1964), 260, 302.
- 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 (1,1,1,1,1,1).
Crossrefs
Programs
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Maple
A000383:=(-1+z**2+2*z**3+3*z**4+4*z**5)/(-1+z**2+z**3+z**4+z**5+z+z**6); # Simon Plouffe in his 1992 dissertation a:= n-> (Matrix([[1$6]]). Matrix(6, (i,j)-> if (i=j-1) or j=1 then 1 else 0 fi)^n)[1,6]: seq(a(n), n=0..28); # Alois P. Heinz, Aug 26 2008
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Mathematica
LinearRecurrence[{1,1,1,1,1,1},{1,1,1,1,1,1},50] (* Harvey P. Dale, Oct 30 2013 *) -
PARI
a(n)=([0,1,0,0,0,0; 0,0,1,0,0,0; 0,0,0,1,0,0; 0,0,0,0,1,0; 0,0,0,0,0,1; 1,1,1,1,1,1]^n*[1;1;1;1;1;1])[1,1] \\ Charles R Greathouse IV, Sep 24 2015
Formula
G.f. ( -1+x^2+2*x^3+3*x^4+4*x^5 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6 ). - R. J. Mathar, Oct 11 2011