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A020956
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Sum of [tau^(n-k)] for k from 1 to infinity.
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7
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1, 2, 4, 8, 14, 25, 42, 71, 117, 193, 315, 514, 835, 1356, 2198, 3562, 5768, 9339, 15116, 24465, 39591, 64067, 103669, 167748, 271429, 439190, 710632, 1149836, 1860482, 3010333, 4870830, 7881179, 12752025, 20633221, 33385263, 54018502, 87403783, 141422304
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OFFSET
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1,2
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..1000
Clark Kimberling, Problem 10520, Amer. Math. Mon. 103 (1996) p. 347.
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,1).
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FORMULA
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G.f.: x*(1-x^2+x^3)/((1-x-x^2)*(1+x)*(1-x)^2). - Ralf Stephan, Apr 08 2004
a(n) = Lucas(n+1) - [n/2] - 1 = sum(k=0, n-1, A014217(k)).
a(n) = 2^(-2-n)*((-2)^n - 5*2^n + 2*(1-t)^(1+n) + 2*(1+t)^n + 2*t*(1+t)^n - 2^(1+n)*n) where t=sqrt(5). - Colin Barker, Feb 09 2017
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MATHEMATICA
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LinearRecurrence[{2, 1, -3, 0, 1}, {1, 2, 4, 8, 14}, 40] (* Vincenzo Librandi, Nov 01 2016 *)
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PROG
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(Python)
prpr = 0
prev = 1
for n in range(2, 100):
print(prev, end=", ")
curr = prpr+prev + n//2
prpr = prev
prev = curr
# Alex Ratushnyak, Jul 30 2012
(PARI) Vec(x*(1-x^2+x^3)/((1-x-x^2)*(1+x)*(1-x)^2) + O(x^50)) \\ Michel Marcus, Nov 01 2016
(Magma)
I:=[1, 2, 4, 8, 14]; [n le 5 select I[n] else 2*Self(n-1)+Self(n-2)-3*Self(n-3)+Self(n-5): n in [1..40]]; // Vincenzo Librandi, Nov 01 2016
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CROSSREFS
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Cf. A014217.
Sequence in context: A340658 A291443 A210145 * A164393 A164391 A164153
Adjacent sequences: A020953 A020954 A020955 * A020957 A020958 A020959
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling
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EXTENSIONS
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More terms from Vladeta Jovovic, Apr 04 2002
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STATUS
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approved
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