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 A195039 #24 Dec 15 2024 15:47:04
%S A195039 0,23,69,138,230,345,483,644,828,1035,1265,1518,1794,2093,2415,2760,
%T A195039 3128,3519,3933,4370,4830,5313,5819,6348,6900,7475,8073,8694,9338,
%U A195039 10005,10695,11408,12144,12903,13685,14490,15318,16169,17043,17940,18860
%N A195039 23 times triangular numbers.
%C A195039 Related to the primitive Pythagorean triple [15, 8, 17].
%C A195039 Sequence found by reading the line from 0, in the direction 0, 23, ..., and the same line from 0, in the direction 0, 69, ..., in the Pythagorean spiral whose edges have length A195035 and whose vertices are the numbers A195036. This is the main diagonal of the square spiral.
%H A195039 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195039 a(n) = (23*n^2 + 23*n)/2 = 23*n*(n+1)/2 = 23*A000217(n).
%F A195039 a(0)=0, a(1)=23, a(2)=69, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Aug 28 2012
%F A195039 From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F A195039 G.f.: 23*x/(1-x)^3.
%F A195039 E.g.f.: 23*exp(x)*x*(2 + x)/2.
%F A195039 a(n) = A069174(n+1) - 1. (End)
%t A195039 23*Accumulate[Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,23,69},50] (* _Harvey P. Dale_, Aug 28 2012 *)
%o A195039 (PARI) a(n)=23*n*(n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195039 Bisection of A195036.
%Y A195039 Cf. A000217, A069174, A195035.
%K A195039 nonn,easy
%O A195039 0,2
%A A195039 _Omar E. Pol_, Sep 12 2011