A352182 Twice A200994.

0, 30, 2970, 291060, 28520940, 2794761090, 273858065910, 26835295698120, 2629585120349880, 257672506498590150, 25249276051741484850, 2474171380564166925180, 242443546019236617182820, 23756993338504624316991210, 2327942903627433946447955790, 228114647562150022127582676240

Offset: 0

Author

N. J. A. Sloane, Mar 08 2022

Keywords

• nonn
• easy

Comments

Also 3 times A200993 and 6 times A352181.

Numbers that both doubles and triples 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, A352181.

Formula

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.: -30*x/((x - 1)*(x^2 - 98*x + 1)). (End)

a(n) = 30*A278620. - Hugo Pfoertner, Apr 22 2024