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A308124
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a(n) = (2 + 7*4^n)/3.
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1
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3, 10, 38, 150, 598, 2390, 9558, 38230, 152918, 611670, 2446678, 9786710, 39146838, 156587350, 626349398, 2505397590, 10021590358, 40086361430, 160345445718, 641381782870, 2565527131478, 10262108525910, 41048434103638, 164193736414550, 656774945658198, 2627099782632790
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OFFSET
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0,1
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COMMENTS
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Consider A092808 and its differences:
1, 0, 3, 1, 11, 5, 43, 21, 171, ...
-1, 3, -2, 10, -6, 38, -22, 150, ... = b(n).
a(n) is the second bisection of b(n). The first is A047849.
a(n) mod 9 is the period 9 sequence: repeat {3, 1, 2, 6, 4, 5, 0, 7, 8].
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 2 for n=1,2,... , a(0) = 3.
Binomial transform of A141495(n+1) = 3, 7, 21, ....
G.f.: (3 - 5*x) / ((1 - x)*(1 - 4*x)).
a(n) = 5*a(n-1) - 4*a(n-2) for n>1.
(End)
a(n+2) = a(n) + 35*A000302(n) for n=0,1,2, ... .
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MATHEMATICA
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LinearRecurrence[{5, -4}, {3, 10}, 30] (* Paolo Xausa, Nov 13 2023 *)
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PROG
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(PARI) Vec((3 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^40)) \\ Colin Barker, Jul 23 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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EXTENSIONS
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STATUS
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approved
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