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
Links
- Paolo Xausa, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,5,-1).
Programs
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Mathematica
LinearRecurrence[{5, 5, -1}, {3, 5, 35}, 25] (* Paolo Xausa, Jul 03 2025 *) -
PARI
my(N=30, x='x+O('x^N)); Vec((3-10*x-5*x^2)/((1+x)*(1-6*x+x^2)))
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.