Search: id:A001590
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%I A001590 M0784 N0296
%S A001590 0,1,0,1,2,3,6,11,20,37,68,125,230,423,778,1431,2632,4841,8904,16377,
%T A001590 30122,55403,101902,187427,344732,634061,1166220,2145013,3945294,
%U A001590 7256527,13346834,24548655,45152016,83047505,152748176,280947697
%N A001590 Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=0, a(1)=1, 
               a(2)=0.
%C A001590 Dimensions of the homogeneous components of the higher order peak algebra 
               associated to cubic roots of unity (Hilbert series = 1+1*t+2*t^2+3*t^3+6*t^4+11*t^5 
               ...) - Jean-Yves Thibon (jyt(AT)univ-mlv.fr), Oct 22 2006
%C A001590 Starting with offset 3: (1, 2, 3, 6, 11, 10, 37,...) = row sums of triangle 
               A145579. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 13 2008]
%C A001590 Starting (1, 2, 3, 6, 1l,...) = INVERT transform of the periodic sequence 
               (1, 1, 0, 1, 1, 0, 1, 1, 0,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               May 04 2009]
%D A001590 M. Feinberg, Fibonacci-Tribonacci, Fib. Quart. 1(#3) (1963), 71-74.
%D A001590 M. Feinberg, New slants, Fib. Quart., 2 (1964), 223-227.
%D A001590 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001590 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001590 M. E. Waddill and L. Sacks, Another generalized Fibonacci sequence, Fib. 
               Quart., 5 (1967), 209-222.
%H A001590 T. D. Noe, <a href="b001590.txt">Table of n, a(n) for n = 0..200</a>
%H A001590 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=401">
               Encyclopedia of Combinatorial Structures 401</a>
%H A001590 D. Krob and J.-Y. Thibon, <a href="http://arXiv.org/abs/math.CO/0411407">
               Higher order peak algebras</a>
%H A001590 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TribonacciNumber.html">Tribonacci Number</a>
%H A001590 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A001590 Limit a(n)/a(n-1)=x where x^3=1+x+x^2, x=1.839286755.... Let T(n)=A000073=0, 
               0, 1, 1, 2, 4, 7, 13... x^0=1 and for n>0 x^n=T(n-1)+a(n)*x+T(n)*x^2.
%F A001590 a(3n)=Sum(k+l+m=n)(n!/k!l!m!)*a(l+2m). Example: a(12)=a(8)+4a(7)+10a(6)+16a(5)+19a(4)+16a(3)+10a(2)+4a(1)+a(0\
               ) The coefficients are the trinomial coefficients. T(n) and T(n-1) 
               also satisfy this equation. (T(-1)=1)
%F A001590 G.f.: x(1-x)/(1-x-x^2-x^3).
%F A001590 a(n)=A000073(n+1)-A000073(n); a(n)=A000073(n-1)+A000073(n-2) for n>1; 
               A000213(n-2)=a(n+1)-a(n) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 22 2006
%F A001590 a(n)+a(n+1)=A000213(n) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Sep 25 2006
%e A001590 a(12)=a(11)+a(10)+a(9): 230=125+68+37
%t A001590 a=0;b=1;c=0;lst={a, b, c};Do[d=a+b+c;AppendTo[lst, d];a=b;b=c;c=d, {n, 
               5!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 
               2008]
%Y A001590 Cf. A000045, A000073, A027907, A001590.
%Y A001590 Cf. A027053, A078042.
%Y A001590 A145579 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 13 2008]
%Y A001590 Sequence in context: A010033 A065615 A054182 this_sequence A078042 A115792 
               A054177
%Y A001590 Adjacent sequences: A001587 A001588 A001589 this_sequence A001591 A001592 
               A001593
%K A001590 nonn,easy
%O A001590 0,5
%A A001590 N. J. A. Sloane (njas(AT)research.att.com).
%E A001590 More terms from Henry Bottomley (se16(AT)btinternet.com), Jun 26 2001
%E A001590 Additional comments from Miklos Kristof (kristmikl(AT)freemail.hu), Jul 
               03 2002

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