%I A001846 M4622 N1974
%S A001846 1,9,41,129,321,681,1289,2241,3649,5641,8361,11969,16641,
%T A001846 22569,29961,39041,50049,63241,78889,97281,118721,143529,
%U A001846 172041,204609,241601,283401,330409,383041,441729,506921
%N A001846 Centered 4-dimensional orthoplex numbers (crystal ball sequence for 4-dimensional 
               cubic lattice).
%C A001846 Number of nodes degree 8 in virtual, optimal, chordal graphs of diameter 
               d(G)=n - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), 
               Mar 07 2002
%C A001846 If Y_i (i=1,2,3,4) are 2-blocks of a (n+4)-set X then a(n-4) is the number 
               of 8-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan R. Janjic 
               (agnus(AT)blic.net), Oct 28 2007
%C A001846 Equals binomial transform of [1, 8, 24, 32, 16, 0, 0, 0,...] where (1, 
               8, 24, 32, 16) = row 4 of the Chebyshev triangle A013609. - Gary 
               W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008
%D A001846 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001846 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001846 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.
%D A001846 R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, 
               SIAM Rev., 12 (1970), 277-279.
%H A001846 T. D. Noe, <a href="b001846.txt">Table of n, a(n) for n=0..1000</a>
%H A001846 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>).
%H A001846 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A001846 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 A001846 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 A001846 <a href="Sindx_Cor.html#crystal_ball">Index entries for crystal ball 
               sequences</a>
%F A001846 G.f.: (1+x)^4 /(1-x)^5.
%F A001846 a(n)=(2*n^4+4*n^3+10*n^2+8*n+3)/3 - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), 
               Mar 07 2002
%F A001846 a(n) = SUM[i=0..n] A008412(i); a(n) = SUM[i=0..n] (8*i)*(i^2+2)/3; a(n) 
               = SUM[i=0..n] (8*i)*(A059100(i))/3 - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Mar 15 2006
%e A001846 a(6)=1289, (2*6^4+4*6^3+10*6^2+8*6+3)/3=(2592+864+360+48+3)/3=3867/3=1289
%p A001846 for n from 1 to k do eval((2*n^4+4*n^3+10*n^2+8*n+3)/3) od;
%p A001846 A001846:=-(z+1)**4/(z-1)**5; [Conjectured (correctly) by S. Plouffe in 
               his 1992 dissertation.]
%Y A001846 Cf. A001847, A008412, A059100.
%Y A001846 Cf. A013609.
%Y A001846 Sequence in context: A000437 A095809 A018836 this_sequence A034441 A056243 
               A083584
%Y A001846 Adjacent sequences: A001843 A001844 A001845 this_sequence A001847 A001848 
               A001849
%K A001846 nonn,easy
%O A001846 0,2
%A A001846 N. J. A. Sloane (njas(AT)research.att.com).