This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195037 #32 Dec 27 2024 18:30:31
%S A195037 0,17,51,102,170,255,357,476,612,765,935,1122,1326,1547,1785,2040,
%T A195037 2312,2601,2907,3230,3570,3927,4301,4692,5100,5525,5967,6426,6902,
%U A195037 7395,7905,8432,8976,9537,10115,10710,11322,11951,12597,13260,13940,14637,15351,16082,16830
%N A195037 17 times triangular numbers.
%C A195037 Related to the primitive Pythagorean triple [5, 12, 13].
%C A195037 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.
%C A195037 Sum of the numbers from 8*n to 9*n. - _Wesley Ivan Hurt_, Dec 23 2015
%H A195037 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195037 a(n) = (17*n^2 + 17*n)/2 = 17*n*(n+1)/2 = 17*A000217(n).
%F A195037 From _Wesley Ivan Hurt_, Dec 23 2015: (Start)
%F A195037 G.f.: 17*x/(1-x)^3.
%F A195037 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F A195037 a(n) = Sum_{i=8*n..9*n} i. (End)
%F A195037 From _Amiram Eldar_, Feb 22 2023: (Start)
%F A195037 Sum_{n>=1} 1/a(n) = 2/17.
%F A195037 Sum_{n>=1} (-1)^(n+1)/a(n) = (4*log(2) - 2)/17.
%F A195037 Product_{n>=1} (1 - 1/a(n)) = -(17/(2*Pi))*cos(5*Pi/(2*sqrt(17))).
%F A195037 Product_{n>=1} (1 + 1/a(n)) = (17/(2*Pi))*cos(3*Pi/(2*sqrt(17))). (End)
%F A195037 From _Elmo R. Oliveira_, Dec 25 2024: (Start)
%F A195037 E.g.f.: 17*exp(x)*x*(2 + x)/2.
%F A195037 a(n) = A195032(2*n). (End)
%p A195037 A195037:=n->17*n*(n+1)/2: seq(A195037(n), n=0..60); # _Wesley Ivan Hurt_, Dec 23 2015
%t A195037 17*Accumulate[Range[0,50]] (* _Harvey P. Dale_, May 31 2014 *)
%t A195037 Table[17*n*(n + 1)/2, {n, 0, 50}] (* _Wesley Ivan Hurt_, Dec 23 2015 *)
%o A195037 (Magma) [17*n*(n+1)/2 : n in [0..50]]; // _Wesley Ivan Hurt_, Dec 23 2015
%o A195037 (PARI) a(n)=17*n*(n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195037 Bisection of A195032.
%Y A195037 Cf. A000217, A195031.
%K A195037 nonn,easy
%O A195037 0,2
%A A195037 _Omar E. Pol_, Sep 12 2011