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A340627
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a(n) = (11*2^n - 2*(-1)^n)/3 for n >= 0.
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2
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3, 8, 14, 30, 58, 118, 234, 470, 938, 1878, 3754, 7510, 15018, 30038, 60074, 120150, 240298, 480598, 961194, 1922390, 3844778, 7689558, 15379114, 30758230, 61516458, 123032918, 246065834, 492131670, 984263338, 1968526678, 3937053354, 7874106710, 15748213418, 31496426838
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OFFSET
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0,1
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COMMENTS
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Prepended with 0, 1, its difference table is
0, 1, 1, 2, 1, 4, 3, 8, ... = mix A001045(n), 2^n.
-1, 1, -2, 4, -4, 6, -8, 14, ... = mix -2^n, A084214(n+1).
2, -3, 6, -8, 10, -14, 22, -30, ... = mix 2*A001045(n+2), -a(n).
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LINKS
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FORMULA
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a(0)=3, a(2*n+1) = 2*a(2*n) + 2, a(2*n+2) = 2*a(2*n+1) - 2, n>=0.
a(n+1) = 11*2^n - a(n) for n>=0.
a(n+3) = 33*2^n - a(n) for n>=0.
a(n+5) = 121*2^n - a(n) for n>=0.
etc.
a(n+2) = a(n) + 11*2^n for n>=0.
a(n+4) = a(n) + 55*2^n for n>=0.
a(n+6) = a(n) + 231*2^n for n>=0.
etc.
E.g.f: (11*exp(2*x) - 2*exp(-x))/3. - Jianing Song, Apr 26 2021
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MATHEMATICA
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LinearRecurrence[{1, 2}, {3, 8}, 35] (* Amiram Eldar, Apr 25 2021 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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