A096019 a(0)=3, a(n) = 3*a(n-1) + 2*(-1)^n.

3, 7, 23, 67, 203, 607, 1823, 5467, 16403, 49207, 147623, 442867, 1328603, 3985807, 11957423, 35872267, 107616803, 322850407, 968551223, 2905653667, 8716961003, 26150883007, 78452649023, 235357947067, 706073841203, 2118221523607

Offset: 0

Author

T. D. Noe, Jun 15 2004

Keywords

• nonn
• easy

Comments

The number of Pythagorean quadruples mod 3^n is given by a(n) 3^(2n-1). See A096018.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Cf. A096018.

Programs

Mathematica

LinearRecurrence[{2,3},{3,7},30] (* Harvey P. Dale, Feb 10 2024 *)

Formula

a(n) = 3^(n+1)-(3^n-(-1)^n)/2.

a(n) = 2*a(n-1)+3*a(n-2). G.f.: (3+x)/((1+x)*(1-3*x)). [Colin Barker, Mar 26 2012]