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A124312
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G.f.: (x^3 - x^4)/(1 - x - x^2 - x^3 - x^4 - x^5).
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3
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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
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OFFSET
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1,6
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COMMENTS
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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
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..3407
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).
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MAPLE
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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
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MATHEMATICA
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CoefficientList[Series[(x^3 - x^4)/(1 - x - x^2 - x^3 - x^4 - x^5), { x, 0, 50}], x]
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CROSSREFS
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Cf. A001591, A124311, A124313, A124314.
Sequence in context: A018088 A189101 A018089 * A068030 A251707 A251712
Adjacent sequences: A124309 A124310 A124311 * A124313 A124314 A124315
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KEYWORD
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nonn,easy
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AUTHOR
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Artur Jasinski, Oct 25 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, Oct 29 2006, Jul 14 2007
Name corrected by Robert Israel, Apr 13 2017
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STATUS
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approved
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