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%I #18 Jun 17 2017 03:17:19
%S 0,41,123,246,410,615,861,1148,1476,1845,2255,2706,3198,3731,4305,
%T 4920,5576,6273,7011,7790,8610,9471,10373,11316,12300,13325,14391,
%U 15498,16646,17835,19065,20336,21648,23001,24395,25830,27306,28823,30381,31980
%N 41 times triangular numbers.
%C Related to the primitive Pythagorean triple [21, 20, 29].
%C Sequence found by reading the line from 0, in the direction 0, 41,..., and the same line from 0, in the direction 0, 123,..., in the Pythagorean spiral whose edges have length A195033 and whose vertices are the numbers A195034. 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) = (41*n^2 + 41*n)/2 = 41*n*(n+1)/2 = 41*A000217(n).
%F G.f.: -41*x / (x-1)^3 . - _R. J. Mathar_, Oct 04 2014
%t 41*Accumulate[Range[0,40]] (* or *) LinearRecurrence[{3,-3,1},{0,41,123},40] (* _Harvey P. Dale_, Nov 20 2015 *)
%o (PARI) a(n)=41*n*(n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Bisection of A195034.
%Y Cf. A000217, A195033.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Sep 12 2011
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