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A136408
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a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).
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1
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1, 2, 4, 7, 13, 27, 55, 107, 211, 427, 859, 1707, 3403, 6827, 13675, 27307, 54571, 109227, 218539, 436907, 873643, 1747627, 3495595, 6990507, 13980331, 27962027, 55925419, 111848107, 223693483, 447392427, 894790315, 1789569707, 3579128491
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..32.
Index entries for linear recurrences with constant coefficients, signature (3,-4,6,-4).
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FORMULA
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From R. J. Mathar, Apr 04 2008: (Start)
O.g.f.: -(-1 + x - 2x^2 + 3x^3)/((x-1)*(2x-1)*(2x^2+1)).
a(n) = 5*2^n/6 + 1/3 - A077966(n)/6. (End)
a(n) = 1/3 + (5/6)*2^n - (1/12)*(i*sqrt(2))^n - (1/12)*(-i*sqrt(2))^n, with n>=0 and i=sqrt(-1). - Paolo P. Lava, Jun 09 2008
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MATHEMATICA
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LinearRecurrence[{3, -4, 6, -4}, {1, 2, 4, 7}, 40] (* Harvey P. Dale, Aug 12 2016 *)
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PROG
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(PARI) a(n)=(5<<n - imag(quadgen(-8)^(n+1)) + 2)/6 \\ Charles R Greathouse IV, Mar 30 2022
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CROSSREFS
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Cf. A077966.
Sequence in context: A112740 A309050 A265580 * A317718 A103104 A103480
Adjacent sequences: A136405 A136406 A136407 * A136409 A136410 A136411
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Mar 31 2008
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EXTENSIONS
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More terms from R. J. Mathar, Apr 04 2008
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STATUS
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approved
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