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A022266 a(n) = n*(9*n - 1)/2. 11
0, 4, 17, 39, 70, 110, 159, 217, 284, 360, 445, 539, 642, 754, 875, 1005, 1144, 1292, 1449, 1615, 1790, 1974, 2167, 2369, 2580, 2800, 3029, 3267, 3514, 3770, 4035, 4309, 4592, 4884, 5185, 5495, 5814, 6142, 6479, 6825, 7180, 7544, 7917, 8299, 8690, 9090, 9499 (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 the line from 0 in the direction 0,4,... - Floor van Lamoen, Jul 21 2001. The spiral begins:

            15

          16  14

        17   3  13

      18   4   2  12

    19   5   0   1  11

  20   6   7   8   9  10

The sequence can be determined by dividing the members of the set of pentagonal numbers (A000326) by 3. Those divisible by 3 result in this sequence. - Richard Torres, Dec 27 2010

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

FORMULA

a(n) = C(9*n,2)/9 for n>=0. - Zerinvary Lajos, Jan 02 2007

a(n) = A049452(n) - A000326(n). - Zerinvary Lajos, Jun 12 2007

a(n) = 9*n + a(n-1) - 5 for n>0, a(0)=0. - Vincenzo Librandi, Aug 04 2010

G.f.: x*(4 + 5*x)/(1 - x)^3. - Colin Barker, Feb 14 2012

a(n) = A218470(9*n+3). - Philippe Deléham, Mar 27 2013

a(n) = A000217(5*n-1) - A000217(4*n-1). - Bruno Berselli, Oct 17 2016

From Wesley Ivan Hurt, Dec 04 2016: (Start)

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

a(n) = (1/7) * Sum_{i=n..(8*n-1)} i. (End)

E.g.f.: (x/2)*(9*x + 8)*exp(x). - G. C. Greubel, Aug 24 2017

MAPLE

[seq(binomial(9*n, 2)/9, n=0..37)]; # Zerinvary Lajos, Jan 02 2007

seq(n*(6*n-1)-n*(3*n-1)/2, n=0..37); # Zerinvary Lajos, Jun 12 2007

MATHEMATICA

Table[n (9 n - 1)/2, {n, 0, 40}] (* Bruno Berselli, Oct 17 2016 *)

PROG

(PARI) a(n)=n*(9*n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015

(MAGMA) [n*(9*n-1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 04 2016

CROSSREFS

Cf. A000217, A000326, A022267, A049452, A051682, A218470, A235332.

Cf. similar sequences listed in A022288.

Sequence in context: A182868 A178947 A041859 * A273309 A145995 A275815

Adjacent sequences:  A022263 A022264 A022265 * A022267 A022268 A022269

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 23 00:33 EST 2018. Contains 299473 sequences. (Running on oeis4.)