A195037 17 times triangular numbers.

0, 17, 51, 102, 170, 255, 357, 476, 612, 765, 935, 1122, 1326, 1547, 1785, 2040, 2312, 2601, 2907, 3230, 3570, 3927, 4301, 4692, 5100, 5525, 5967, 6426, 6902, 7395, 7905, 8432, 8976, 9537, 10115, 10710, 11322, 11951, 12597, 13260, 13940, 14637, 15351, 16082, 16830

Offset

0,2

Comments

Related to the primitive Pythagorean triple [5, 12, 13].

Sequence found by reading the line from 0, in the direction 0, 17, ..., and the same line from 0, in the direction 0, 51, ..., in the Pythagorean spiral whose edges have length A195031 and whose vertices are the numbers A195032. This is the main diagonal of the square spiral.

Sum of the numbers from 8n to 9n. - Wesley Ivan Hurt, Dec 23 2015

Links

Table of n, a(n) for n=0..44.

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

Formula

a(n) = (17*n^2 + 17*n)/2 = 17*n*(n+1)/2 = 17*A000217(n).

From Wesley Ivan Hurt, Dec 23 2015: (Start)

G.f.: 17*x/(1-x)^3.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>2.

a(n) = Sum_{i=8n..9n} i. (End)

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 2/17.

Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/17.

Product_{n>=1} (1 - 1/a(n)) = -(17/(2*Pi))*cos(5*Pi/(2*sqrt(17))).

Product_{n>=1} (1 + 1/a(n)) = (17/(2*Pi))*cos(3*Pi/(2*sqrt(17))). (End)

Maple

A195037:=n->17*n*(n+1)/2: seq(A195037(n), n=0..60); # Wesley Ivan Hurt, Dec 23 2015

Mathematica

17*Accumulate[Range[0, 50]] (* Harvey P. Dale, May 31 2014 *)
Table[17*n*(n + 1)/2, {n, 0, 50}] (* Wesley Ivan Hurt, Dec 23 2015 *)

Prog

(Magma) [17*n*(n+1)/2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 23 2015
(PARI) a(n)=17*n*(n+1)/2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Bisection of A195032.

Cf. A000217, A195031.

Sequence in context: A160076 A003124 A005570 * A214660 A258598 A223906

Adjacent sequences: A195034 A195035 A195036 * A195038 A195039 A195040

Keyword

nonn,easy

Author

Omar E. Pol, Sep 12 2011

Status

approved