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%I #19 Jun 17 2017 03:17:21
%S 0,23,69,138,230,345,483,644,828,1035,1265,1518,1794,2093,2415,2760,
%T 3128,3519,3933,4370,4830,5313,5819,6348,6900,7475,8073,8694,9338,
%U 10005,10695,11408,12144,12903,13685,14490,15318,16169,17043,17940,18860
%N 23 times triangular numbers.
%C Related to the primitive Pythagorean triple [15, 8, 17].
%C 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F a(n) = (23*n^2 + 23*n)/2 = 23*n*(n+1)/2 = 23*A000217(n).
%F 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
%t 23*Accumulate[Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,23,69},50] (* _Harvey P. Dale_, Aug 28 2012 *)
%o (PARI) a(n)=23*n*(n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Bisection of A195036.
%Y Cf. A000217, A195035.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Sep 12 2011
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