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

0,1

Comments

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

Links

Table of n, a(n) for n=0..25.

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

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

From Klaus Purath, May 28 2026: (Start)

a(n) = 10*3^(n-1) - a(n-1).

a(n) = 20*3^(n-2) + a(n-2).

a(n) = (5*3^n + (-1)^n)/2.

a(n) = A321573(n+1) + (-1)^n.

a(n) = A137340(n) + 2*(-1)^n. (End)

Mathematica

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

Crossrefs

Cf. A096018, A137340, A321573.

Sequence in context: A148692 A201204 A106964 * A148693 A148694 A148695

Adjacent sequences: A096016 A096017 A096018 * A096020 A096021 A096022

Keyword

nonn,easy,changed

Author

T. D. Noe, Jun 15 2004

Status

approved