A051871 19-gonal (or enneadecagonal) numbers: n(17n-15)/2.

0, 1, 19, 54, 106, 175, 261, 364, 484, 621, 775, 946, 1134, 1339, 1561, 1800, 2056, 2329, 2619, 2926, 3250, 3591, 3949, 4324, 4716, 5125, 5551, 5994, 6454, 6931, 7425, 7936, 8464, 9009, 9571, 10150, 10746, 11359, 11989, 12636, 13300

Offset

0,3

Comments

Sequence found by reading the line from 0, in the direction 0, 19, ... and the parallel line from 1, in the direction 1, 54, ..., in the square spiral whose vertices are the generalized 19-gonal numbers. - Omar E. Pol, Jul 18 2012

Partial sums of A215137 (17n + 1). - Jeremy Gardiner, Aug 04 2012

References

Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.

Elena Deza and Michel M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.

Links

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

Index to sequences related to polygonal numbers

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = n(17n-15)/2.

G.f.: x*(1+16*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011

a(n) = 17*n + a(n-1) - 16 (with a(0) = 0). - Vincenzo Librandi, Aug 06 2010

a(17*a(n) + 137*n + 1) = a(17*a(n) + 137*n) + a(17*n+1). - Vladimir Shevelev, Jan 24 2014

Product_{n>=2} (1 - 1/a(n)) = 17/19. - Amiram Eldar, Jan 22 2021

E.g.f.: exp(x)*(x + 17*x^2/2). - Nikolaos Pantelidis, Feb 06 2023

Example

a(1) = 17 * 1 + 0 - 16 = 1.
a(2) = 17 * 2 + 1 - 16 = 19.
a(3) = 17 * 3 + 19 - 16 = 54. - Vincenzo Librandi, Aug 06 2010

Maple

A051871 := proc(n) n*(17*n-15)/2 ; end proc: seq(A051871(n), n=0..30) ; # R. J. Mathar, Feb 05 2011

Mathematica

Table[(17n^2 - 15n)/2, {n, 0, 39}] (* Alonso del Arte, Feb 19 2015 *)

Prog

(PARI) a(n)=n*(17*n-15)/2; \\ Charles R Greathouse IV, Jan 24 2014

Crossrefs

Sequence in context: A142072 A221594 A288144 * A371110 A371056 A044121

Adjacent sequences: A051868 A051869 A051870 * A051872 A051873 A051874

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 15 1999

Status

approved