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A022940
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a(n) = a(n-1) + b(n-2) for n >= 3, a( ) increasing, given a(1) = 1, a(2) = 3; where b( ) is complement of a( ).
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10
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1, 3, 5, 9, 15, 22, 30, 40, 51, 63, 76, 90, 106, 123, 141, 160, 180, 201, 224, 248, 273, 299, 326, 354, 383, 414, 446, 479, 513, 548, 584, 621, 659, 698, 739, 781, 824, 868, 913, 959, 1006, 1054, 1103, 1153, 1205, 1258, 1312, 1367, 1423, 1480
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OFFSET
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1,2
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COMMENTS
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The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. The initial values of each sequence in the following guide are a(0) = 1, a(2) = 3, b(0) = 2, b(1) = 4:
here: a(n) = a(n-1) + b(n-2) [with a different offset]
A294397: a(n) = a(n-1) + b(n-2) + 1;
A294398: a(n) = a(n-1) + b(n-2) + 2;
A294399: a(n) = a(n-1) + b(n-2) + 3;
A294400: a(n) = a(n-1) + b(n-2) + n;
A294401: a(n) = a(n-1) + b(n-2) + 2*n.
(End)
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LINKS
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EXAMPLE
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a(1) = 1, a(2) = 3, b(1) = 2, b(2) = 4, so that a(3) = a(2) + a(1) + b(2) = 5.
Complement: {b(n)} = {2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, ...}
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MATHEMATICA
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Fold[Append[#1, #1[[-1]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {1, 3}, Range[50]] (* Ivan Neretin, Apr 04 2016 *)
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CROSSREFS
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Cf. A005228 and references therein.
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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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