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A124313 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), starting 1,0,0,0,1.

%I A124313 #22 Feb 16 2025 08:33:03
%S A124313 1,0,0,0,1,2,3,6,12,24,47,92,181,356,700,1376,2705,5318,10455,20554,
%T A124313 40408,79440,156175,307032,603609,1186664,2332920,4586400,9016625,
%U A124313 17726218,34848827,68510990,134689060,264791720,520566815,1023407412
%N A124313 Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), starting 1,0,0,0,1.
%H A124313 G. C. Greubel, <a href="/A124313/b124313.txt">Table of n, a(n) for n = 1..1000</a>
%H A124313 I. Flores, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/5-3/flores.pdf">k-Generalized Fibonacci numbers</a>, Fib. Quart., 5 (1967), 258-266.
%H A124313 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentanacciNumber.html">Pentanacci Number</a>
%H A124313 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1).
%F A124313 G.f.: x*(1-x-x^2-x^3)/(1-x-x^2-x^3-x^4-x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009; checked and corrected by _R. J. Mathar_, Sep 16 2009
%t A124313 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, 4]]; Array[f, 50]
%t A124313 LinearRecurrence[{1,1,1,1,1}, {1,0,0,0,1}, 40] (* _G. C. Greubel_, Aug 25 2023 *)
%o A124313 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1-2*x+x^4)/(1-2*x+x^6) )); // _G. C. Greubel_, Aug 25 2023
%o A124313 (SageMath)
%o A124313 def A124313_list(prec):
%o A124313     P.<x> = PowerSeriesRing(ZZ, prec)
%o A124313     return P( (1-2*x+x^4)/(1-2*x+x^6) ).list()
%o A124313 A124313_list(50) # _G. C. Greubel_, Aug 25 2023
%Y A124313 Cf. A001591, A124312, A124314.
%K A124313 nonn,easy
%O A124313 1,6
%A A124313 _Artur Jasinski_, Oct 25 2006
%E A124313 Edited by _Ralf Stephan_, Oct 20 2013