A215137 -id:A215137 - cp's OEIS frontend

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

N. J. A. Sloane, Dec 15 1999

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

			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

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.

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).

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

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

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

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

A154612 a(n) = 17*n + 7.

Original entry on oeis.org

7, 24, 41, 58, 75, 92, 109, 126, 143, 160, 177, 194, 211, 228, 245, 262, 279, 296, 313, 330, 347, 364, 381, 398, 415, 432, 449, 466, 483, 500, 517, 534, 551, 568, 585, 602, 619, 636, 653, 670, 687, 704, 721, 738, 755, 772, 789, 806, 823, 840, 857, 874, 891

Offset: 0

Vincenzo Librandi, Jan 15 2009

a(n)^4 = Sum_{j=0..(16*n*(17*n+14)+46)} (-1)^j*(119*n^2 + 98*n + 20 + j)^2. - Bruno Berselli, Apr 30 2010

			For n=5, a(5)^4 = 92^4 = 71639296 = 3485^2-3486^2+3487^2-..+11449^2-11450^2+11451^2. - _Bruno Berselli_, Apr 30 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A138629, A138630.

Sequences of the form 17*n+q: A361692 (q=-1), A008599 (q=0), A215137 (q=1), this sequence (q=7).

I:=[7, 24]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Feb 21 2012

Range[7, 1000, 17] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)

for(n=0, 50, print1(17*n + 7", ")); \\ Vincenzo Librandi, Feb 26 2012

[17*n+7 for n in range(61)] # G. C. Greubel, May 31 2024

G.f.: (7+10*x)/(1-x)^2. - Colin Barker, Jan 09 2012
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Feb 26 2012
E.g.f.: (7 + 17*x)*exp(x). - G. C. Greubel, May 31 2024

Offset corrected by Bruno Berselli, Aug 16 2010

cp's OEIS Frontend

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

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