

A124312


G.f.: (x^3  x^4)/(1  x  x^2  x^3  x^4  x^5).


3



0, 0, 1, 0, 1, 2, 4, 8, 15, 30, 59, 116, 228, 448, 881, 1732, 3405, 6694, 13160, 25872, 50863, 99994, 196583, 386472, 759784, 1493696, 2936529, 5773064, 11349545, 22312618, 43865452, 86237208, 169537887, 333302710, 655255875, 1288199132
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,6


COMMENTS

Second column of the nth power of pentanacci matrix {{1,1,1,1,1},{1,0,0,0,0}, {0,1,0,0,0}, {0,0,1,0,0}, {0,0,0,1,0}} read from bottom to top gives 5 numbers starting from position n.
a(n+5) equals the number of nlength binary words avoiding runs of zeros of lengths 5i+4, (i=0,1,2,...).  Milan Janjic, Feb 26 2015


LINKS

Robert Israel, Table of n, a(n) for n = 1..3407
Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, Analytic Representations of the nanacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).


MAPLE

f:= gfun:rectoproc({a(n)+a(n+1)+a(n+2)+a(n+3)+a(n+4)a(n+5), a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 1, a(4) = 0}, a(n), remember):
seq(f(n), n=1..30); # Robert Israel, Apr 13 2017


MATHEMATICA

CoefficientList[Series[(x^3  x^4)/(1  x  x^2  x^3  x^4  x^5), { x, 0, 50}], x]


CROSSREFS

Cf. A001591, A124311, A124313, A124314.
Sequence in context: A018088 A189101 A018089 * A068030 A251707 A251712
Adjacent sequences: A124309 A124310 A124311 * A124313 A124314 A124315


KEYWORD

nonn,easy


AUTHOR

Artur Jasinski, Oct 25 2006


EXTENSIONS

Edited by N. J. A. Sloane, Oct 29 2006, Jul 14 2007
Name corrected by Robert Israel, Apr 13 2017


STATUS

approved



