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A322417
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a(n) - 2*a(n-1) = period 2: repeat [3, 0] for n > 0, a(0)=5, a(1)=13.
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1
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5, 13, 26, 55, 110, 223, 446, 895, 1790, 3583, 7166, 14335, 28670, 57343, 114686, 229375, 458750, 917503, 1835006, 3670015, 7340030, 14680063, 29360126, 58720255, 117440510, 234881023, 469762046, 939524095, 1879048190, 3758096383, 7516192766
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OFFSET
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0,1
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COMMENTS
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a(n) mod 9 = period 6: repeat [5, 4, 8, 1, 2, 7]. See A177883(n+2).
a(n+1) mod 10 = period 4: repeat [3, 6, 5, 0].
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LINKS
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FORMULA
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a(n) = a(n-2) + 21*2^(n-2) for n >= 2.
a(n) = a(n-1) + A321483(n) for n > 0.
G.f.: (5 + 3*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)).
a(n) = 7*2^n - 2 for n even.
a(n) = 7*2^n - 1 for n odd.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n > 2.
(End)
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MATHEMATICA
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a[0] = 5; a[1] = 13; a[n_] := a[n] = a[n - 2] + 21*2^(n - 2); Array[a, 30, 0] (* Amiram Eldar, Dec 07 2018 *)
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PROG
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(GAP) a:=[13, 26];; for n in [3..30] do a[n]:=a[n-2]+21*2^(n-2); od; Concatenation([5], a); # Muniru A Asiru, Dec 07 2018
(PARI) Vec((5 + 3*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Dec 07 2018
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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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