A383720 a(0)=3, a(1)=5, a(2)=35; a(n) = 5*a(n-1) + 5*a(n-2) - a(n-3) for n > 2.

3, 5, 35, 197, 1155, 6725, 39203, 228485, 1331715, 7761797, 45239075, 263672645, 1536796803, 8957108165, 52205852195, 304278004997, 1773462177795, 10336495061765, 60245508192803, 351136554095045, 2046573816377475, 11928306344169797, 69523264248641315

Offset

0,1

Comments

Let (t) be any recurrence of the form (5,5,-1) or of the form (6,-1). Then the following always applies: a(n) = (t(i+3*n) - (-1)^n*t(i))/(t(i+2*n) - (-1)^n*t(i+n)) regardless of initial values as long as t(i+2*n) - (-1)^n*t(i+n) != 0 for n >= 1 and any integer i. - Klaus Purath, Sep 07 2025

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,5,-1).

Formula

G.f.: (3 - 10*x - 5*x^2)/((1 + x) * (1 - 6*x + x^2)).

a(n) = Pell(3*n)/Pell(n) for n > 0.

Mathematica

LinearRecurrence[{5, 5, -1}, {3, 5, 35}, 25] (* Paolo Xausa, Jul 03 2025 *)

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec((3-10*x-5*x^2)/((1+x)*(1-6*x+x^2)))

Crossrefs

Cf. A000129, A002203, A047946, A084158.

Sequence in context: A120828 A077784 A325582 * A145640 A222496 A086158

Adjacent sequences: A383717 A383718 A383719 * A383721 A383722 A383723

Keyword

nonn,easy

Author

Seiichi Manyama, May 07 2025

Status

approved