0,2

Number of nodes of degree 12 in virtual, optimal chordal graphs of diameter d(G)=n - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Nov 25 2002

Equals binomial transform of [1, 12, 60, 160, 240, 192, 64, 0, 0, 0,...] where (1, 12, 60, 160, 240, 192, 64) = row 6 of the Chebyshev triangle A013609. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 19 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 81.

R. G. Stanton and D. D. Cowan, Note on a "square" functional equation, SIAM Rev., 12 (1970), 277-279.

T. D. Noe, Table of n, a(n) for n=0..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).

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.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

Index entries for crystal ball sequences

G.f.: (1+x)^6 /(1-x)^7.

a(n) = 4/45*n^6+4/15*n^5+14/9*n^4+8/3*n^3+196/45*n^2+46/15*n+1 - S. Bujnowski & B. Dubalski (slawb(AT)atr.bydgoszcz.pl), Nov 25 2002

for n from 1 to k do eval(4/45*n^6+4/15*n^5+14/9*n^4+8/3*n^3+196/45*n^2+46/15*n+1); od;

A001848:=-(z+1)**6/(z-1)**7; [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

Cf. A001847, A013609.

Sequence in context: A142085 A163688 A010025 this_sequence A055843 A003764 A082036

Adjacent sequences: A001845 A001846 A001847 this_sequence A001849 A001850 A001851

nonn,easy

N. J. A. Sloane (njas(AT)research.att.com).