A370481 a(0) = 33. a(n) = 3*a(n-1) + 2*n + 1 for n >= 1.

33, 102, 311, 940, 2829, 8498, 25507, 76536, 229625, 688894, 2066703, 6200132, 18600421, 55801290, 167403899, 502211728, 1506635217, 4519905686, 13559717095, 40679151324, 122037454013, 366112362082, 1098337086291, 3295011258920, 9885033776809, 29655101330478

Offset: 0

Author

Paul Curtz, Mar 31 2024

Keywords

• nonn
• easy

Comments

Last digit is of period 10: repeat [3, 2, 1, 0, 9, 8, 7, 6, 5, 4].

Examples

			a(1) = 3*33 + 3 = 102, a(2) = 3*102 + 5 = 311.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Crossrefs

Cf. A144396, A237930.

Programs

Mathematica

LinearRecurrence[{5, -7, 3}, {33, 102, 311}, 26] (* Amiram Eldar, Apr 01 2024 *)

Formula

a(n) = 4*a(n-1) - 3*a(n-2) + 2 with a(0) = 33 and a(1) = 102 for n >= 2.

a(n) = 10*A237930(n) + 3 - n.

a(n) = 35*3^n - n - 2. - Hugo Pfoertner, Mar 31 2024