|
| |
|
|
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 S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 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] ];
|
|
|
CROSSREFS
|
Cf. A000045, A000288, A000383, A060455.
Sequence in context: A180565 A160426 A059743 * A205539 A020737 A147401
Adjacent sequences: A000319 A000320 A000321 * A000323 A000324 A000325
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
STATUS
|
approved
|
| |
|
|
