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A292035
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Linear divisibility sequence based on Salem number of order 4 (case t=7, see formula).
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1
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1, 7, 41, 245, 1476, 8897, 53621, 323155, 1947541, 11737152, 70735741, 426299755, 2569160621, 15483439097, 93313311876, 562366934045, 3389190268241, 20425473083407, 123097234932601, 741864297888000, 4470958562003401, 26944915020252607, 162387648058027841, 978653976900562445
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = round(lambda(7)*alpha(7)^n)
where alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4
and lambda(t) = 1/sqrt((t-4)*t+8).
G.f.: x*(1 - x)*(1 + x) / (1 - 7*x + 7*x^2 - 7*x^3 + x^4).
a(n) = 7*a(n-1) - 7*a(n-2) + 7*a(n-3) - a(n-4) for n>4.
(End)
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MATHEMATICA
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alpha[t_] := (t + Sqrt[(t - 4) t + 8] + Sqrt[2] Sqrt[t (t + Sqrt[(t - 4) t + 8] - 2) - 4])/4;
lambda[t_] := 1/Sqrt[(t - 4) t + 8];
a[n_] := Round[lambda[7] alpha[7]^n] ;
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PROG
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(PARI) alpha(t) = (t+sqrt((t-4)*t+8)+sqrt(2)*sqrt(t*(t+sqrt((t-4)*t+8)-2)-4))/4;
lambda(t) = 1/sqrt((t-4)*t+8);
a(n) = my(ca=alpha(7), cl=lambda(7)); round(cl*ca^n);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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