A271226 a(n) = (A271222(n)^2 + 2)/3^n, n >= 0.

2, 2, 3, 1, 43, 201, 67, 1289, 2278, 14662, 53782, 171798, 57266, 312537, 104179, 7353209, 14081926, 94917254, 148495259, 338541478, 2498895558, 832965186, 277655062, 45869694854, 90480235883, 230874654662

Offset: 0

Author

Wolfdieter Lang, Apr 05 2016

Keywords

• nonn
• easy

Comments

a(n) is an integer because b(n) = A271222(n) satisfies b(n)^2 + 2 == 0 (mod 3^n), n >= 0.

See A268924 for details, links and references.

Examples

			a(0) = (0^2 + 2)/1 = 2.
a(4) = (59^2 + 2)/3^4 = 43.
		

Crossrefs

Cf. A268924, A271222, A271224, A271225 (companion sequence).

Programs

PARI

b(n) = if (n, 3^n - truncate(sqrt(-2+O(3^(n)))), 0);
a(n) = (b(n)^2 + 2)/3^n; \\ Michel Marcus, Apr 09 2016

Formula

a(n) = (b(n)^2 + 2)/3^n, n >= 0, with b(n) = A271222(n).