This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A005915 Hexagonal prism numbers: a(n) = (n + 1)*(3*n^2 + 3*n + 1). (Formerly M4933) 15
 1, 14, 57, 148, 305, 546, 889, 1352, 1953, 2710, 3641, 4764, 6097, 7658, 9465, 11536, 13889, 16542, 19513, 22820, 26481, 30514, 34937, 39768, 45025, 50726, 56889, 63532, 70673, 78330, 86521, 95264, 104577, 114478, 124985, 136116, 147889 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 07 2004 a(n) is the number of 4-tuples (w,x,y,z) with all terms in {0,...,n} and w=x or x=y or y=z. - Clark Kimberling, May 31 2012 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992. Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992. Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA a(n)=(n+1)^3 + 6* (n*(n+1)*(2*n+1)/6). - Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de) a(0)=1, a(1)=14, a(2)=57, a(3)=148, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Jun 25 2011 G.f.: (1+10*x+7*x^2)/(1-x)^4. - Harvey P. Dale, Jun 25 2011 Equals row sums of triangle A143804 and binomial transform of [1, 13, 30, 18, 0, 0, 0,...]. - Gary W. Adamson, Sep 01 2008 2*a(n+1) = A213829(n). - Clark Kimberling, Jul 04 2012 MAPLE A005915:=(1+10*z+7*z**2)/(z-1)**4; [Conjectured by Simon Plouffe in his 1992 dissertation.] MATHEMATICA Table[(n+1)(3n^2+3n+1), {n, 0, 50}]  (* Harvey P. Dale, Mar 31 2011 *) LinearRecurrence[{4, -6, 4, -1}, {1, 14, 57, 148}, 50] (* Harvey P. Dale, Jun 25 2011 *) PROG (MAGMA) [(n + 1)*(3*n^2 + 3*n + 1): n in [0..50]]; // Vincenzo Librandi, May 16 2011 (PARI) a(n) = (n + 1)*(3*n^2 + 3*n + 1); CROSSREFS Cf. A143804. Cf. A260260 (comment). [Bruno Berselli, Jul 22 2015] Sequence in context: A041374 A070741 A022286 * A211069 A212675 A041376 Adjacent sequences:  A005912 A005913 A005914 * A005916 A005917 A005918 KEYWORD nonn,easy,nice AUTHOR EXTENSIONS More terms from James A. Sellers, Dec 24 1999 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 12:42 EDT 2019. Contains 327307 sequences. (Running on oeis4.)