|
| |
|
|
A000383
|
|
Hexanacci numbers with a(0) = ... = a(5) = 1.
(Formerly M4088 N1697)
|
|
43
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
