A022940 - OEIS

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A022940

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( ).

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

1,2

COMMENTS

From Clark Kimberling, Oct 30 2017: (Start)

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)

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13.

EXAMPLE

a(1) = 1, a(2) = 3, b(1) = 2, b(2) = 4, so that a(3) = a(2) + a(1) + b(2) = 5.