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A051682 11-gonal (or hendecagonal) numbers: n(9n-7)/2. 73
0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, 606, 715, 833, 960, 1096, 1241, 1395, 1558, 1730, 1911, 2101, 2300, 2508, 2725, 2951, 3186, 3430, 3683, 3945, 4216, 4496, 4785, 5083, 5390, 5706, 6031, 6365, 6708, 7060, 7421, 7791, 8170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 0,1,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:

......15

....16..14

..17..3...13

18..4...2...12

..5...0...1...11

6...7...8...9...10

(1), (4+7), (7+10+13), (10+13+16+19), ... - Jon Perry, Sep 10 2004

This sequence does not contain any triangular numbers other than 0 and 1. See A188892. - T. D. Noe, Apr 13 2011

Sequence found by reading the line from 0, in the direction 0, 11,... and the parallel line from 1, in the direction 1, 30,..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - Omar E. Pol, Jul 18 2012

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.

Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.

LINKS

T. D. Noe, Table of n, a(n) for n=0..1000

Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

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

Row sums of triangle A131432 - Gary W. Adamson, Jul 10 2007

a(n)=9*n+a(n-1)-8 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]

a(0)=0, a(1)=1, a(2)=11, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, May 07 2012]

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

a(9*a(n)+37*n+1) = a(9*a(n)+37*n) + a(9*n+1). - Vladimir Shevelev, Jan 24 2014

MAPLE

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+9 od: seq(a[n], n=0..43); - Zerinvary Lajos, Feb 18 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 9}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 15 2008]

Table[n (9n-7)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 11}, 51] (* Harvey P. Dale, May 07 2012 *)

PROG

(PARI) a(n)=(9*n-7)*n/2 \\ Charles R Greathouse IV, Jun 16 2011

CROSSREFS

First differences of A007586.

Cf. A093644 ((9, 1) Pascal, column m=2). Partial sums of A017173.

Cf. A004188.

Cf. A131432.

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, this sequence, A051624, A051865-A051876.

Sequence in context: A146751 A162734 A163060 * A109943 A137411 A002755

Adjacent sequences:  A051679 A051680 A051681 * A051683 A051684 A051685

KEYWORD

nonn,easy,changed

AUTHOR

Barry E. Williams

EXTENSIONS

More terms from James A. Sellers, Dec 08 1999

STATUS

approved

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Last modified April 24 11:13 EDT 2014. Contains 240983 sequences.