Search: id:A000574
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%I A000574 M3011 N1219
%S A000574 3,16,51,126,266,504,882,1452,2277,3432,5005,7098,9828,13328,17748,
%T A000574 23256,30039,38304,48279,60214,74382,91080,110630,133380,159705,190008,
%U A000574 224721,264306,309256,360096,417384,481712,553707,634032,723387,822510
%N A000574 Coefficient of x^5 in expansion of (1+x+x^2)^n.
%C A000574 G.f.: x^3*(3-2*x)/(1-x)^6. 3*binomial(n+2,5)-2*binomial(n+1,5)
%C A000574 a(n) = A111808(n,5) for n>4. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Aug 17 2005
%C A000574 If Y is a 3-subset of an n-set X then, for n>=7, a(n-4) is the number 
               of 5-subsets of X having at most one element in common with Y. - 
               Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007
%D A000574 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000574 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000574 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A000574 L. Carlitz et al., Permutations and sequences with repetions by number 
               of increases, J. Combin. Theory, 1 (1966), 350-374.
%D A000574 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
%H A000574 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A000574 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A000574 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TrinomialCoefficient.html">Trinomial Coefficient</a>
%F A000574 a(n)= binomial(n+1, 4)*(n+12)/5 = 3*b(n-3)-2*b(n-4), with b(n):=binomial(n+5, 
               5); cf. A000389.
%p A000574 A000574:=-(-3+2*z)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
%Y A000574 Cf. A005581, A005712, A005714-A005716.
%Y A000574 Column m=5 of (1, 3) Pascal triangle A095660.
%Y A000574 Cf. A005712, A000581.
%Y A000574 Sequence in context: A152618 A004320 A089363 this_sequence A041233 A055194 
               A027540
%Y A000574 Adjacent sequences: A000571 A000572 A000573 this_sequence A000575 A000576 
               A000577
%K A000574 nonn,easy
%O A000574 3,1
%A A000574 N. J. A. Sloane (njas(AT)research.att.com).
%E A000574 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 02 2000

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