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A349072
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a(n) = T(n, 3*n), where T(n, x) is the Chebyshev polynomial of the first kind.
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5
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1, 3, 71, 2889, 164737, 12082575, 1083358151, 114812765781, 14040770918401, 1946133989077851, 301491888156044999, 51624542295308885793, 9681761035138427706241, 1973656779656041723763559, 434528364117341972641648967, 102755067271708508826774929325
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OFFSET
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0,2
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COMMENTS
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In general, for k>=1, T(n, k*n) ~ 2^(n-1) * k^n * n^n.
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LINKS
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FORMULA
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a(n) = cosh(n*arccosh(3*n)).
a(n) = ((3*n + sqrt(9*n^2-1))^n + (3*n - sqrt(9*n^2-1))^n)/2.
a(n) ~ 2^(n-1) * 3^n * n^n.
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MATHEMATICA
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Table[ChebyshevT[n, 3*n], {n, 0, 20}]
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PROG
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(PARI) a(n) = polchebyshev(n, 1, 3*n); \\ Michel Marcus, Nov 07 2021
(Python)
from sympy import chebyshevt
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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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