A051869 17-gonal (or heptadecagonal) numbers: a(n) = n*(15*n-13)/2.

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

Offset: 0

Author

N. J. A. Sloane, Dec 15 1999

Keywords

• nonn
• easy

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

• Albert 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 related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A002378.

Programs

GAP

List([0..40], n-> n*(15*n-13)/2); # G. C. Greubel, Aug 30 2019

Magma

[n*(15*n-13)/2: n in [0..40]]; // G. C. Greubel, Aug 30 2019

Maple

A051869 := proc(n) n*(15*n-13)/2 ; end proc: seq(A051869(n),n=0..30) ; # R. J. Mathar, Feb 05 2011

Mathematica

Table[n*(15*n - 13)/2, {n,0,40}] (* Robert Price, Oct 11 2018 *)
PolygonalNumber[17,Range[0,50]] (* Harvey P. Dale, Dec 14 2022 *)

PARI

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

Sage

[n*(15*n-13)/2 for n in (0..40)] # G. C. Greubel, Aug 30 2019

Formula

G.f.: x*(1+14*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = a(n-1) + 15*n - 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

E.g.f.: x*(2 + 15*x)*exp(x)/2. - G. C. Greubel, Aug 30 2019

Product_{n>=2} (1 - 1/a(n)) = 15/17. - Amiram Eldar, Jan 22 2021