Search: id:A006503
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%I A006503 M2835
%S A006503 0,3,10,22,40,65,98,140,192,255,330,418,520,637,770,920,1088,
%T A006503 1275,1482,1710,1960,2233,2530,2852,3200,3575,3978,4410,4872,
%U A006503 5365,5890,6448,7040,7667,8330,9030,9768,10545,11362,12220
%N A006503 n(n+1)(n+8)/6.
%C A006503 If Y is a 3-subset of an n-set X then, for n>=4, a(n-4) is the number 
               of 3-subsets of X having at most one element in common with Y. - 
               Milan R. Janjic (agnus(AT)blic.net), Nov 23 2007
%C A006503 The coefficient of x^3 in (1-x-x^2)^{-n} is the coefficient of x^3 in 
               (1+x+2x^2+3x^3)^n. Using the multinomial theorem one then finds that 
               a(n)=n(n+1)(n+8)/3! - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 
               22 2008
%D A006503 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006503 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, 
               pp. 194-196.
%D A006503 G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient 
               array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 
               43-48.
%H A006503 P. Moree, <a href="http://arXiv.org/abs/math.CO/0311205">Convoluted convolved 
               Fibonacci numbers</a>
%H A006503 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 A006503 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.
%F A006503 a(n)=n*(n+1)*(n+8)/6. G.f.: x*(3-2*x)/(1-x)^4.
%F A006503 a(n) = A000292(n) + A0002378(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Sep 24 2008]
%p A006503 A006503:=-(-3+2*z)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]
%t A006503 Clear["Global`*"] a[n_] := n(n + 1)(n + 8)/3! Do[Print[n, " ", a[n]], 
               {n, 1, 25}] - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), May 22 2008
%Y A006503 a(n) = A095660(n+2, 3): fourth column of (1, 3)-Pascal triangle.
%Y A006503 Cf. A000027, A000096, A006504.
%Y A006503 Sequence in context: A161672 A122795 A140066 this_sequence A023554 A070880 
               A027164
%Y A006503 Adjacent sequences: A006500 A006501 A006502 this_sequence A006504 A006505 
               A006506
%K A006503 nonn,easy
%O A006503 0,2
%A A006503 N. J. A. Sloane (njas(AT)research.att.com).
%E A006503 Better description from Jeffrey Shallit 8/95.

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