login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000383 Hexanacci numbers with a(0) = ... = a(5) = 1.
(Formerly M4088 N1697)
41

%I M4088 N1697

%S 1,1,1,1,1,1,6,11,21,41,81,161,321,636,1261,2501,4961,9841,19521,

%T 38721,76806,152351,302201,599441,1189041,2358561,4678401,9279996,

%U 18407641,36513081,72426721,143664401,284970241,565262081,1121244166,2224080691,4411648301

%N Hexanacci numbers with a(0) = ... = a(5) = 1.

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

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

%H Indranil Ghosh, <a href="/A000383/b000383.txt">Table of n, a(n) for n = 0..3358</a> (terms 0..200 from T. D. Noe)

%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>

%H B. G. Baumgart, Letter to the editor <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-a.pdf">Part 1</a> <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-b.pdf">Part 2</a> <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-c.pdf">Part 3</a>, Fib. Quart. 2 (1964), 260, 302.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1).

%F 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

%p 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.]

%p 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

%t LinearRecurrence[{1,1,1,1,1,1},{1,1,1,1,1,1},50] (* _Harvey P. Dale_, Oct 30 2013 *)

%o (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

%Y Cf. A060455.

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

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

%Y Cf. A249413 (primes in this sequence).

%K nonn,easy

%O 0,7

%A _N. J. A. Sloane_.

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 25 16:34 EST 2020. Contains 338625 sequences. (Running on oeis4.)