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%I M4088 N1697 #64 Nov 30 2023 10:35:06
%S 1,1,1,1,1,1,6,11,21,41,81,161,321,636,1261,2501,4961,9841,19521,
%T 38721,76806,152351,302201,599441,1189041,2358561,4678401,9279996,
%U 18407641,36513081,72426721,143664401,284970241,565262081,1121244166,2224080691,4411648301
%N Hexanacci numbers with a(0) = ... = a(5) = 1.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Indranil Ghosh, <a href="/A000383/b000383.txt">Table of n, a(n) for n = 0..3358</a> (terms 0..200 from T. D. Noe)
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>
%H B. G. Baumgart, Letter to the editor <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-a.pdf">Part 1</a> <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-b.pdf">Part 2</a> <a href="http://www.fq.math.ca/Scanned/2-4/baumgart-c.pdf">Part 3</a>, Fib. Quart. 2 (1964), 260, 302.
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1).
%F 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
%p 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
%p 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
%t LinearRecurrence[{1,1,1,1,1,1},{1,1,1,1,1,1},50] (* _Harvey P. Dale_, Oct 30 2013 *)
%o (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
%Y Cf. A060455.
%Y Cf. A001592 (Hexanacci numbers with a(0) = ... = a(4) = 0 and a(5)=1).
%Y Cf. A247192 (indices of primes in this sequence).
%Y Cf. A249413 (primes in this sequence).
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_
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