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A343177
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a(0)=4; if n > 0 is even then a(n) = 2^(n/2+1)+3, otherwise a(n) = 3*(2^((n-1)/2)+1).
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21
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4, 6, 7, 9, 11, 15, 19, 27, 35, 51, 67, 99, 131, 195, 259, 387, 515, 771, 1027, 1539, 2051, 3075, 4099, 6147, 8195, 12291, 16387, 24579, 32771, 49155, 65539, 98307, 131075, 196611, 262147, 393219, 524291, 786435, 1048579, 1572867, 2097155, 3145731, 4194307, 6291459
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OFFSET
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0,1
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COMMENTS
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Number of edges along the boundary of the graph G(n) described in A342759.
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LINKS
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FORMULA
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G.f.: (4 + 2*x - 7*x^2 - 2*x^3)/((1 - x)*(1 - 2*x^2)). - Stefano Spezia, Feb 04 2023
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MAPLE
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f:=n->if n = 0 then 4 elif (n mod 2) = 0 then 2^(n/2+1)+3 else 3*(2^((n-1)/2)+1); fi;
[seq(f(n), n=0..40)];
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MATHEMATICA
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LinearRecurrence[{1, 2, -2}, {4, 6, 7, 9}, 50] (* or *)
A343177[n_] := Which[n == 0, 4, OddQ[n], 3*(2^((n-1)/2)+1), True, 2^(n/2+1)+3];
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CROSSREFS
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The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022
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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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