Search: id:A001847
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%I A001847 M4793 N2045
%S A001847 1,11,61,231,681,1683,3653,7183,13073,22363,36365,56695,
%T A001847 85305,124515,177045,246047,335137,448427,590557,766727,
%U A001847 982729,1244979,1560549,1937199,2383409,2908411,3522221
%N A001847 Crystal ball sequence for 5-dimensional cubic lattice.
%C A001847 Number of nodes degree 10 in virtual, optimal chordal graphs of diameter 
               d(G)=n - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), 
               Mar 07 2002
%C A001847 If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-5) is the 
               number of 10-subsets of X intersecting each Y_i (i=1,2,3,4,5). - 
               Milan R. Janjic (agnus(AT)blic.net), Oct 28 2007
%C A001847 Equals binomial transform of [1, 10, 40, 80, 80, 32, 0, 0, 0,...] where 
               (1, 10, 40, 80, 80, 32) = row 5 of the Chebyshev triangle A013609. 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008
%D A001847 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001847 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001847 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 A001847 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.
%D A001847 R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, 
               SIAM Rev., 12 (1970), 277-279.
%H A001847 T. D. Noe, <a href="b001847.txt">Table of n, a(n) for n=0..1000</a>
%H A001847 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A001847 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 A001847 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 A001847 <a href="Sindx_Cor.html#crystal_ball">Index entries for crystal ball 
               sequences</a>
%H A001847 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination 
               Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http:/
               /www.research.att.com/~njas/doc/ldl7.txt">Abstract</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.pdf">pdf</a>, <a href="http:/
               /www.research.att.com/~njas/doc/ldl7.ps">ps</a>).
%F A001847 G.f.: (1+x)^5 /(1-x)^6.
%F A001847 a(n)=(4*n^5+10*n^4+40*n^3+50*n^2+46*n+15)/15 - S. Bujnowski & B. Dubalski 
               (slawb(AT)atr.bydgoszcz.pl), Mar 07 2002
%e A001847 a(5)=1683, (4*5^5+10*5^4+40*5^3+50*5^2+46*5+15)/15=(12500+6250+5000+230+15)/
               15=25245/15=1683
%p A001847 for n from 1 to k do eval((4*n^5+10*n^4+40*n^3+50*n^2+46*n+15)/15) od;
%p A001847 A001847:=(z+1)**5/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
%Y A001847 Cf. A013609.
%Y A001847 Sequence in context: A002650 A060884 A141935 this_sequence A089764 A023298 
               A106992
%Y A001847 Adjacent sequences: A001844 A001845 A001846 this_sequence A001848 A001849 
               A001850
%K A001847 nonn,easy
%O A001847 0,2
%A A001847 N. J. A. Sloane (njas(AT)research.att.com).

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