0,2

Also as a(n)=(1/6)*(18*n^3-18*n^2+6*n), n>0: structured rhombic dodecahedral numbers (vertex structure 7) (A100157 = alternate vertex); structured tetrakis hexahedral numbers (vertex structure 7) (Cf. A100174 = alternate vertex); and structured hexagonal anti-diamond numbers (vertex structure 7) (Cf. A007588 = alternate vertex) (Cf. A100188 = structured anti-diamonds). Cf. A100145 for more on structured polyhedral numbers. - James A. Record (james.record(AT)gmail.com), Nov. 7, 2004.

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

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.

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

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.

a(n)=(n+1)^3 + 6* (n*(n+1)*(2*n+1)/6) - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de).

Equals row sums of triangle A143804 and binomial transform of [1, 13, 30, 18, 0, 0, 0,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

A005915:=(1+10*z+7*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]

A143804 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]

Sequence in context: A041374 A070741 A022286 this_sequence A041376 A063537 A084195

Adjacent sequences: A005912 A005913 A005914 this_sequence A005916 A005917 A005918

nonn,easy,nice

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

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999