login
This site is supported by donations to The OEIS Foundation.

 

Logo

Many excellent designs for a new banner were submitted. We will use the best of them in rotation.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A000322 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) with a(0)=a(1)=a(2)=a(3)=a(4)=1.
(Formerly M3786 N1542)
29
1, 1, 1, 1, 1, 5, 9, 17, 33, 65, 129, 253, 497, 977, 1921, 3777, 7425, 14597, 28697, 56417, 110913, 218049, 428673, 842749, 1656801, 3257185, 6403457, 12588865, 24749057, 48655365, 95653929, 188050673, 369697889, 726806913, 1428864769 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

For n>=0: a(n+2) is the number of length-n strings with letters {0,1,2,3,4} where the letter x is followed by at least x zeros, see fxtbook link below. [Joerg Arndt, Apr 08 2011]

REFERENCES

B. G. Baumgart, Letter to the editor, Fib. Quart. 2 (1964), 260, 302.

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

T. D. Noe, Table of n, a(n) for n = 0..200

Joerg Arndt, Fxtbook, pp.311-312

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

MAPLE

A000322:=(-1+z**2+2*z**3+3*z**4)/(-1+z**2+z**3+z+z**4+z**5); [Simon Plouffe in his 1992 dissertation.]

a:= n-> (Matrix([[1$5]]). Matrix(5, (i, j)-> if (i=j-1) or j=1 then 1 else 0 fi)^n)[1, 5]: seq (a(n), n=0..28); # Alois P. Heinz, Aug 26 2008

MATHEMATICA

LinearRecurrence[{1, 1, 1, 1, 1}, {1, 1, 1, 1, 1}, 50]

PROG

(MAGMA) [ n le 5 select 1 else Self(n-1)+Self(n-2)+Self(n-3)+Self(n-4)+Self(n-5): n in [1..40] ];

(PARI) Vec((1-x^2-2*x^3-3*x^4)/(1-x-x^2-x^3-x^4-x^5)+O(x^99)) \\ Charles R Greathouse IV, Jul 01 2013

CROSSREFS

Cf. A000045, A000288, A000383, A060455.

Sequence in context: A233187 A160426 A059743 * A205539 A020737 A147401

Adjacent sequences:  A000319 A000320 A000321 * A000323 A000324 A000325

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified April 16 00:41 EDT 2014. Contains 240534 sequences.