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A051869 17-gonal (or heptadecagonal) numbers: n(15n-13)/2. 10
0, 1, 17, 48, 94, 155, 231, 322, 428, 549, 685, 836, 1002, 1183, 1379, 1590, 1816, 2057, 2313, 2584, 2870, 3171, 3487, 3818, 4164, 4525, 4901, 5292, 5698, 6119, 6555, 7006, 7472, 7953, 8449, 8960, 9486, 10027, 10583, 11154, 11740, 12341 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence found by reading the line from 0, in the direction 0, 17,... and the parallel line from 1, in the direction 1, 48,..., in the square spiral whose vertices are the generalized 17-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

Ivan Panchenko, 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+14*x)/(1-x)^3. [Bruno Berselli, Feb 04 2011]

a(n) = 15*n+a(n-1)-14 with n>0, a(0)=0. [Vincenzo Librandi, Aug 06 2010]

a(n) = A226489(n) - n. [Bruno Berselli, Jun 11 2013]

a(15*a(n)+106*n+1) = a(15*a(n)+106*n) + a(15*n+1). - Vladimir Shevelev, Jan 24 2014

MAPLE

A051869 := proc(n) n*(15*n-13)/2 ; end proc: seq(A051869(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!, 15}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

PROG

(PARI) a(n)=n*(15*n-13)/2 \\ Charles R Greathouse IV, Jan 24 2014

CROSSREFS

Cf. A002378.

Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051868, this sequence, A051870-A051876.

Sequence in context: A083296 A159850 A031122 * A210372 A239130 A181426

Adjacent sequences:  A051866 A051867 A051868 * A051870 A051871 A051872

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 15 1999

STATUS

approved

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Last modified October 23 06:00 EDT 2014. Contains 248411 sequences.