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A097830
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Partial sums of Chebyshev sequence S(n,16) = U(n,16/2) = A077412(n).
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4
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1, 17, 272, 4336, 69105, 1101345, 17552416, 279737312, 4458244577, 71052175921, 1132376570160, 18046972946640, 287619190576081, 4583860076270657, 73054142029754432, 1164282412399800256, 18555464456367049665, 295723148889472994385, 4713014917775200860496
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = sum(S(k, 16), k=0..n) with S(k, 16) = U(k, 8) = A077412(k) Chebyshev's polynomials of the second kind.
G.f.: 1/((1-x)*(1-16*x+x^2)) = 1/(1-17*x+17*x^2-x^3).
a(n) = 17*a(n-1)-17*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=17.
a(n) = 16*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1.
a(n) = (S(n+1, 16) - S(n, 16) -1)/14.
a(n) = (-6+(45-17*sqrt(7))*(8-3*sqrt(7))^n+(8+3*sqrt(7))^n*(45+17*sqrt(7)))/84. - Colin Barker, Mar 04 2016
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MATHEMATICA
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LinearRecurrence[{17, -17, 1}, {1, 17, 272}, 30] (* or *) Accumulate[ ChebyshevU[Range[0, 30], 8]] (* Harvey P. Dale, Nov 09 2011 *)
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PROG
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(PARI) Vec(1/((1-x)*(1-16*x+x^2)) + O(x^25)) \\ Colin Barker, Mar 04 2016
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CROSSREFS
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Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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