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A062741 3 times pentagonal numbers: 3*n*(3*n-1)/2. 25
0, 3, 15, 36, 66, 105, 153, 210, 276, 351, 435, 528, 630, 741, 861, 990, 1128, 1275, 1431, 1596, 1770, 1953, 2145, 2346, 2556, 2775, 3003, 3240, 3486, 3741, 4005, 4278, 4560, 4851, 5151, 5460, 5778, 6105, 6441, 6786, 7140, 7503, 7875, 8256, 8646, 9045 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Write 0,1,2,3,4,... in a triangular spiral; then a(n) is the sequence found by reading from 0 in the vertical upward direction.

Number of edges in the join of two complete graphs of order 2n and n, K_2n * K_n - Roberto E. Martinez II, Jan 07 2002

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

Franck Ramaharo, A generating polynomial for the pretzel knot, arXiv:1805.10680 [math.CO], 2018.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = binomial(3*n, 2). - Zerinvary Lajos, Jan 02 2007

a(n) = (9*n^2 - 3*n)/2 = 3*n(3*n-1)/2 = A000326(n)*3. - Omar E. Pol, Dec 11 2008

a(n) = 9*n + a(n-1) - 6, with n > 0, a(0)=0. - Vincenzo Librandi, Aug 07 2010

G.f.: 3*x*(1+2*x)/(1-x)^3. - Bruno Berselli, Jan 21 2011

a(n) = A218470(9n+2). - Philippe Deléham, Mar 27 2013

a(n) = n*A008585(n) + Sum_{i=0..n-1} A008585(i) for n > 0. - Bruno Berselli, Dec 19 2013

EXAMPLE

The spiral begins:

            15

          16  14

        17   3  13

      18   4   2  12

    19   5   0   1  11

  20   6   7   8   9  10

MAPLE

[seq(binomial(3*n, 2), n=0..45)]; # Zerinvary Lajos, Jan 02 2007

MATHEMATICA

3*PolygonalNumber[5, Range[0, 50]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 06 2019 *)

PROG

(PARI) a(n)=3*n*(3*n-1)/2 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Cf. A000326, A008585, A051682.

Cf. 3 times n-gonal numbers: A045943, A033428, A094159, A152773, A152751, A152759, A152767, A153783, A153448, A153875.

Sequence in context: A162441 A001803 A161738 * A185541 A176661 A117561

Adjacent sequences:  A062738 A062739 A062740 * A062742 A062743 A062744

KEYWORD

nonn,easy

AUTHOR

Floor van Lamoen, Jul 21 2001

EXTENSIONS

Better definition and edited by Omar E. Pol, Dec 11 2008

STATUS

approved

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Last modified October 18 03:16 EDT 2019. Contains 328135 sequences. (Running on oeis4.)