%I A005915 M4933
%S A005915 1,14,57,148,305,546,889,1352,1953,2710,3641,4764,6097,7658,9465,11536,
%T A005915 13889,16542,19513,22820,26481,30514,34937,39768,45025,50726,56889,
%U A005915 63532,70673,78330,86521,95264,104577,114478,124985,136116,147889
%N A005915 Hexagonal prism numbers: (n + 1)(3n^2 + 3n + 1).
%C A005915 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.
%D A005915 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005915 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 A005915 B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral 
               clusters, Inorgan. Chem. 24 (1985), 4545-4558.
%H A005915 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 A005915 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 A005915 a(n)=(n+1)^3 + 6* (n*(n+1)*(2*n+1)/6) - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de).
%F A005915 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]
%p A005915 A005915:=(1+10*z+7*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%Y A005915 A143804 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
%Y A005915 Sequence in context: A041374 A070741 A022286 this_sequence A041376 A063537 
               A084195
%Y A005915 Adjacent sequences: A005912 A005913 A005914 this_sequence A005916 A005917 
               A005918
%K A005915 nonn,easy,nice
%O A005915 0,2
%A A005915 N. J. A. Sloane (njas(AT)research.att.com).
%E A005915 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 24 1999