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%I #18 Apr 22 2024 13:34:35
%S 0,5,495,48510,4753490,465793515,45643010985,4472549283020,
%T 438264186724980,42945417749765025,4208212675290247475,
%U 412361896760694487530,40407257669872769530470,3959498889750770719498535,387990483937905657741325965,38019107927025003687930446040
%N a(n) = A200993(n)/2.
%C Halves of triangular numbers which are also thirds of triangular numbers.
%H Editors, L'Intermédiaire des Mathématiciens, <a href="/A072256/a072256.pdf">Query 4500: The equation x(x+1)/2 = y*(y+1)/3</a>, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (I).
%H Editors, L'Intermédiaire des Mathématiciens, <a href="/A072256/a072256_1.pdf">Query 4500: The equation x(x+1)/2 = y*(y+1)/3</a>, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (II).
%H Editors, L'Intermédiaire des Mathématiciens, <a href="/A072256/a072256_2.pdf">Query 4500: The equation x(x+1)/2 = y*(y+1)/3</a>, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (III).
%H Editors, L'Intermédiaire des Mathématiciens, <a href="/A072256/a072256_3.pdf">Query 4500: The equation x(x+1)/2 = y*(y+1)/3</a>, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (IV).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).
%F a(n) = A200994(n)/3.
%F From _Chai Wah Wu_, Apr 22 2024: (Start)
%F a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3) for n > 2.
%F G.f.: -5*x/((x - 1)*(x^2 - 98*x + 1)). (End)
%F a(n) = 5*A278620(n). - _Hugo Pfoertner_, Apr 22 2024
%Y Cf. A200993, A200994, A278620.
%K nonn,easy,changed
%O 0,2
%A _N. J. A. Sloane_, Mar 08 2022
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