A352181 a(n) = A200993(n)/2.

0, 5, 495, 48510, 4753490, 465793515, 45643010985, 4472549283020, 438264186724980, 42945417749765025, 4208212675290247475, 412361896760694487530, 40407257669872769530470, 3959498889750770719498535, 387990483937905657741325965, 38019107927025003687930446040

Offset: 0

Author

N. J. A. Sloane, Mar 08 2022

Keywords

• nonn
• easy

Comments

Halves of triangular numbers which are also thirds of triangular numbers.

Links

• Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (I).
• Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (II).
• Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (III).
• Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (IV).
• Index entries for linear recurrences with constant coefficients, signature (99,-99,1).

Crossrefs

Cf. A200993, A200994, A278620.

Formula

a(n) = A200994(n)/3.

From Chai Wah Wu, Apr 22 2024: (Start)

a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3) for n > 2.

G.f.: -5*x/((x - 1)*(x^2 - 98*x + 1)). (End)

a(n) = 5*A278620(n). - Hugo Pfoertner, Apr 22 2024