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A124312 G.f.: (x^3 + x^2 + x + 1)/(1 - x - x^2 - x^3 - x^4 - x^5). 2
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 n-th 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 n-length binary words avoiding runs of zeros of lengths 5i+4, (i=0,1,2,...). - Milan Janjic, Feb 26 2015

LINKS

Table of n, a(n) for n=1..36.

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci 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).

MATHEMATICA

f[n_] := MatrixPower[{{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}}, n][[ 1, 3]]; Array[f, 50]

CoefficientList[Series[(x^3 + x^2 + x + 1)/(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

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.