A000383 Hexanacci numbers with a(0) = ... = a(5) = 1. (Formerly M4088 N1697)

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

0,7

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).

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

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

Mathematica

LinearRecurrence[{1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1}, 50] (* Harvey P. Dale, Oct 30 2013 *)

Prog

(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

Crossrefs

Cf. A060455.

Cf. A001592 (Hexanacci numbers with a(0) = ... = a(4) = 0 and a(5)=1).

Cf. A247192 (indices of primes in this sequence).

Cf. A249413 (primes in this sequence).

Sequence in context: A208670 A208726 A192750 * A205540 A083575 A302869

Adjacent sequences: A000380 A000381 A000382 * A000384 A000385 A000386

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved