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A329244
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Sum of every third term of the Padovan sequence A000931.
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1
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1, 2, 3, 5, 10, 22, 50, 115, 266, 617, 1433, 3330, 7740, 17992, 41825, 97230, 226031, 525457, 1221538, 2839730, 6601570, 15346787, 35676950, 82938845, 192809421, 448227522, 1042002568, 2422362080, 5631308625, 13091204282, 30433357675, 70748973085, 164471408186
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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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G.f.: (1 - 2*x) / ((1 - x)*(1 - 3*x + 2*x^2 - x^3)).
a(n) = 4*a(n-1) - 5*a(n-2) + 3*a(n-3) - a(n-4) for n>3.
(End)
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EXAMPLE
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For n = 3, a(n) = 1+1+1+2 = 5.
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PROG
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(Python)
p = lambda x:[1, 0, 0][x] if x<3 else p(x-2)+p(x-3)
a = lambda x:sum(p(3*i) for i in range(x+1))
(PARI) Vec((1 - 2*x) / ((1 - x)*(1 - 3*x + 2*x^2 - x^3)) + O(x^35)) \\ Colin Barker, Nov 09 2019
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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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STATUS
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approved
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