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A051867 15-gonal (or pentadecagonal) numbers: n(13n-11)/2. 6
0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242, 2490, 2751, 3025, 3312, 3612, 3925, 4251, 4590, 4942, 5307, 5685, 6076, 6480, 6897, 7327, 7770, 8226, 8695, 9177, 9672, 10180, 10701 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 15,... and the parallel line from 1, in the direction 1, 42,..., in the square spiral whose vertices are the generalized 15-gonal numbers. - 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

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: x*(1+12*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = 13*n+a(n-1)-12 (with a(0)=0) - Vincenzo Librandi, Aug 06 2010

a(0)=0, a(1)=1, a(2)=15, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Feb 29 2012

a(13*a(n)+79*n+1) = a(13*a(n)+79*n) + a(13*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]+13 od: seq(a[n], n=0..41); - Zerinvary Lajos, Feb 18 2008

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 13}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)

Table[n (13n-11)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 15}, 50] (* Harvey P. Dale, Feb 29 2012 *)

CROSSREFS

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, A051866, this sequence, A051868-A051876.

Sequence in context: A070007 A154267 A173351 * A008976 A233302 A072119

Adjacent sequences:  A051864 A051865 A051866 * A051868 A051869 A051870

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified December 22 20:35 EST 2014. Contains 252372 sequences.