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A051865 13-gonal (or tridecagonal) numbers: n(11n-9)/2. 47
0, 1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, 738, 871, 1015, 1170, 1336, 1513, 1701, 1900, 2110, 2331, 2563, 2806, 3060, 3325, 3601, 3888, 4186, 4495, 4815, 5146, 5488, 5841, 6205, 6580, 6966, 7363, 7771, 8190, 8620, 9061, 9513 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 13,... and the parallel line from 1, in the direction 1, 36,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313. - Omar E. Pol, Jul 18 2012

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.

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

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) = 11*n+a(n-1)-10 with n>0, a(0)=0. [Vincenzo Librandi, Aug 06 2010]

G.f.: x*(1+10*x)/(1-x)^3. [Bruno Berselli, Feb 04 2011]

a(11*a(n)+56*n+1) = a(11*a(n)+56*n) + a(11*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]+11 od: seq(a[n], n=0..42); - Zerinvary Lajos, Feb 18 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 11}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)

CoefficientList[Series[x (1 + 10 x) / (1 - x)^3, {x, 0, 40}], x] (* _ Vincenzo Librandi_, Jun 19 2013 *)

LinearRecurrence[{3, -3, 1}, {0, 1, 13}, 50] (* Harvey P. Dale, Jul 12 2014 *)

PROG

(PARI) a(n)=(11*n^2-9*n)/2 \\ Charles R Greathouse IV, May 27 2011

CROSSREFS

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, this sequence, A051866-A051876.

Sequence in context: A034119 A054285 A101103 * A081928 A034129 A243038

Adjacent sequences:  A051862 A051863 A051864 * A051866 A051867 A051868

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified September 19 18:34 EDT 2014. Contains 246978 sequences.