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A062708 Write 0,1,2,3,4,... in a triangular spiral; then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,2,... 9
0, 2, 13, 33, 62, 100, 147, 203, 268, 342, 425, 517, 618, 728, 847, 975, 1112, 1258, 1413, 1577, 1750, 1932, 2123, 2323, 2532, 2750, 2977, 3213, 3458, 3712, 3975, 4247, 4528, 4818, 5117, 5425, 5742, 6068, 6403, 6747, 7100, 7462, 7833, 8213, 8602, 9000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Milan Janjic, Two Enumerative Functions

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

FORMULA

a(n) = n*(9*n-5)/2.

a(n) = 9*n + a(n-1) - 7 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

From Colin Barker, Jul 07 2012: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

G.f.: x*(2+7*x)/(1-x)^3. (End)

a(n) = A218470(9n+1). - Philippe Deléham, Mar 27 2013

E.g.f.:  x*(4 + 9*x)*exp(x)/2. - G. C. Greubel, Sep 02 2019

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

.

From Vincenzo Librandi, Aug 07 2010: (Start)

a(1) = 9*1 +  0 - 7 =  2;

a(2) = 9*2 +  2 - 7 = 13;

a(3) = 9*3 + 13 - 7 = 33. (End)

MAPLE

seq(n*(9*n-5)/2, n=0..50); # G. C. Greubel, Sep 02 2019

MATHEMATICA

Table[n*(9*n-5)/2, {n, 0, 50}] (* G. C. Greubel, Sep 02 2019 *)

PROG

(PARI) a(n)=n*(9*n-5)/2 \\ Charles R Greathouse IV, Jun 17 2017

(MAGMA) [n*(9*n-5)/2: n in [0..50]]; // G. C. Greubel, Sep 02 2019

(Sage) [n*(9*n-5)/2 for n in (0..50)] # G. C. Greubel, Sep 02 2019

(GAP) List([0..50], n-> n*(9*n-5)/2); # G. C. Greubel, Sep 02 2019

CROSSREFS

Cf. A051682.

Cf. A218470.

Cf. numbers of the form n*(n*k-k+4))/2 listed in A226488 (this is case k=9).

Sequence in context: A084828 A100512 A051474 * A296293 A190816 A084910

Adjacent sequences:  A062705 A062706 A062707 * A062709 A062710 A062711

KEYWORD

nonn,easy

AUTHOR

Floor van Lamoen, Jul 21 2001

STATUS

approved

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)