login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A051870 18-gonal (or octadecagonal) numbers: a(n) = n*(8*n-7). 21
0, 1, 18, 51, 100, 165, 246, 343, 456, 585, 730, 891, 1068, 1261, 1470, 1695, 1936, 2193, 2466, 2755, 3060, 3381, 3718, 4071, 4440, 4825, 5226, 5643, 6076, 6525, 6990, 7471, 7968, 8481, 9010, 9555, 10116, 10693, 11286, 11895, 12520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 18,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Apr 26 2008

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

Also sequence found by reading the line from 0, in the direction 0, 18,... and the parallel line from 1, in the direction 1, 51,..., in the square spiral whose vertices are the generalized 18-gonal numbers. - Omar E. Pol, Jul 18 2012.

Partial sums of 16n + 1 (with offset 0), compare A005570. - Jeremy Gardiner, Aug 04 2012

All x values for Diophantine equation 32*x + 49 = y^2 are given by this sequence and A139278. - Bruno Berselli, Nov 11 2014

This is also a star enneagonal number: a(n) = A001106(n) + 9*A000217(n-1). - Luciano Ancora, Mar 30 2015

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

Jeremy Gardiner, Table of n, a(n) for n = 0..999

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Wikipedia, Polygonal number.

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

FORMULA

G.f.: x*(1+15*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = 16*n + a(n-1) - 15, with n > 0, a(0) = 0. - Vincenzo Librandi, Aug 06 2010

a(16*a(n)+121*n+1) = a(16*a(n)+121*n) + a(16*n+1). - Vladimir Shevelev, Jan 24 2014

MAPLE

A051870 := proc(n) n*(8*n-7) ; end proc: seq(A051870(n), n=0..30) ; # R. J. Mathar, Feb 05 2011

MATHEMATICA

Table[n (8 n - 7), {n, 0, 40}] (* Bruno Berselli, Nov 11 2014 *)

PROG

(PARI) a(n)=n*(8*n-7) \\ Charles R Greathouse IV, Jul 19 2011

CROSSREFS

Cf. A014634, A014635, A033585, A033586, A033587, A035008, A069129, A085250, A129271 - A129278, A139278.

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051869, this sequence, A051871-A051876.

Sequence in context: A074173 A092068 A093520 * A175815 A069130 A124711

Adjacent sequences:  A051867 A051868 A051869 * A051871 A051872 A051873

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 24 05:56 EDT 2015. Contains 257784 sequences.