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A295060
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Solution of the complementary equation a(n) = 2*a(n-1) - b(n-2), where a(0) = 3, a(1) = 5, b(0) = 1, b(1) = 2, and (a(n)) and (b(n)) are increasing complementary sequences.
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2
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3, 5, 9, 16, 28, 50, 93, 178, 346, 681, 1350, 2687, 5360, 10705, 21393, 42768, 85517, 171014, 342007, 683992, 1367961, 2735898, 5471771, 10943516, 21887005, 43773981, 87547932, 175095833, 350191634
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OFFSET
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0,1
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COMMENTS
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The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A295053 for a guide to related sequences.
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LINKS
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EXAMPLE
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a(0) = 1, a(1) = 4, b(0) = 2, b(1) = 3
a(2) = 2*a(1) - b(0) = 9
Complement: (b(n)) = (1, 2, 4, 6, 7, 8, 10, 11, 12, 13, 14, ...)
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MATHEMATICA
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mex := First[Complement[Range[1, Max[#1] + 1], #1]] &;
a[0] = 3; a[1] = 5; b[0] = 1; b[1]=2;
a[n_] := a[n] = 2 a[n - 1] - b[n - 2];
b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
Table[a[n], {n, 0, 18}] (* A295060 *)
Table[b[n], {n, 0, 10}]
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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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