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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

Table of n, a(n) for n=0..40.

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: A065792 A118546 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 February 19 10:03 EST 2020. Contains 332041 sequences. (Running on oeis4.)