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
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
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
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 12 2011
STATUS
approved