A062728 Second 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n+7)/2.

0, 8, 25, 51, 86, 130, 183, 245, 316, 396, 485, 583, 690, 806, 931, 1065, 1208, 1360, 1521, 1691, 1870, 2058, 2255, 2461, 2676, 2900, 3133, 3375, 3626, 3886, 4155, 4433, 4720, 5016, 5321, 5635, 5958, 6290, 6631, 6981, 7340, 7708, 8085, 8471, 8866, 9270

Offset

0,2

Comments

Old name: 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 0,8,...

Sequence found by reading the line from 0, in the direction 0, 25, ... and the line from 8, in the direction 8, 51, ..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - Omar E. Pol, Jul 24 2012

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = n*(9*n+7)/2.

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

From Bruno Berselli, Jan 13 2011: (Start)

G.f.: x*(8 + x)/(1 - x)^3.

a(n) = Sum_{i=0..n-1} A017257(i) for n > 0. (End)

a(n) = A218470(9n+7). - Philippe Deléham, Mar 27 2013

E.g.f.: x*(16 + 9*x)*exp(x)/2. - G. C. Greubel, May 24 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

Mathematica

Table[n*(9*n+7)/2, {n, 0, 50}] (* G. C. Greubel, May 24 2019 *)
LinearRecurrence[{3, -3, 1}, {0, 8, 25}, 50] (* Harvey P. Dale, Sep 06 2019 *)

Prog

(PARI) a(n)=n*(9*n+7)/2 \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [n*(9*n+7)/2: n in [0..50]]; // G. C. Greubel, May 24 2019
(Sage) [n*(9*n+7)/2 for n in (0..50)] # G. C. Greubel, May 24 2019
(GAP) List([0..50], n-> n*(9*n+7)/2) # G. C. Greubel, May 24 2019

Crossrefs

Cf. A051682.

Second n-gonal numbers: A005449, A014105, A147875, A045944, A179986, A033954, this sequence, A135705.

Sequence in context: A344714 A164754 A204467 * A273982 A244942 A143371

Adjacent sequences: A062725 A062726 A062727 * A062729 A062730 A062731

Keyword

nonn,easy

Author

Floor van Lamoen, Jul 21 2001

Extensions

New name from Bruno Berselli (with the original formula), Jan 13 2011

Status

approved