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 A062783 a(n) = 3*n*(4*n-1). 1
 0, 9, 42, 99, 180, 285, 414, 567, 744, 945, 1170, 1419, 1692, 1989, 2310, 2655, 3024, 3417, 3834, 4275, 4740, 5229, 5742, 6279, 6840, 7425, 8034, 8667, 9324, 10005, 10710, 11439, 12192, 12969, 13770, 14595, 15444, 16317, 17214, 18135, 19080 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Write 1,2,3,4,... counterclockwise in a hexagonal spiral around 0 starting left down, then a(n) is the sequence found by reading from 0 in the vertical downward direction. Polygonal number connection: 2He_n + 7S_n where He_n is the n-th Heptagonal number and S_n is the n-th Square number. - William A. Tedeschi, Sep 12 2010 REFERENCES L. Berzolari, Allgemeine Theorie der Höeren Ebenen Algebraischen Kurven, Encyclopädie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen. Band III_2. Heft 3, Leipzig: B. G. Teubner, 1906. p. 341. LINKS Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 24*n+a(n-1)-15 with n>0, a(0)=0. - Vincenzo Librandi, Aug 07 2010 G.f.: 3*x*(3+5*x)/(1-x)^3. - Colin Barker, Feb 28 2012 EXAMPLE The spiral begins: ......16..15..14 ....17..5...4...13 ..18..6...0...3...12 19..7...1...2...11..26 ..20..8...9...10..25 ....21..22..23..24 MATHEMATICA s=0; lst={s}; Do[s+=n++ +9; AppendTo[lst, s], {n, 0, 8!, 24}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 17 2008 *) PROG (PARI) a(n)=3*n*(4*n-1) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A063436, A000567. Equals 3*A033991(n). Sequence in context: A334147 A336984 A075233 * A172464 A269053 A027441 Adjacent sequences:  A062780 A062781 A062782 * A062784 A062785 A062786 KEYWORD easy,nonn AUTHOR Floor van Lamoen, Jul 21 2001 STATUS approved

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Last modified September 18 01:54 EDT 2021. Contains 347504 sequences. (Running on oeis4.)