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A051870 18-gonal (or octadecagonal) numbers: n(8n-7). 19
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.

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.

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

FORMULA

a(n) = n(8n-7).

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

a(n) = 16*n+a(n-1)-15 (with a(0)=0) [From 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

EXAMPLE

a(2)=16*2+1-15=18; a(3)=16*3+18-15=51 [From Vincenzo Librandi, Aug 06 2010]

MAPLE

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

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 16}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]

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, A129272, A129273, A129274, A129275, A129276, A129277, A129278.

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

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Last modified August 20 02:49 EDT 2014. Contains 245794 sequences.