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

Author

Floor van Lamoen, Jul 21 2001

Keywords

• nonn
• easy

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

Examples

			The spiral begins:
          15
          / \
        16  14
        /     \
      17   3  13
      /   / \   \
    18   4   2  12
    /   /     \   \
  19   5   0---1  11
  /   /             \
20   6---7---8---9--10
		

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051682.

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

Programs

GAP

List([0..50], n-> n*(9*n+7)/2); # G. C. Greubel, May 24 2019

Magma

[n*(9*n+7)/2: n in [0..50]]; // G. C. Greubel, May 24 2019

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 *)

PARI

a(n)=n*(9*n+7)/2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[n*(9*n+7)/2 for n in (0..50)] # G. C. Greubel, May 24 2019

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

Extensions

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