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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( ). 6
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 (list; graph; refs; listen; history; text; internal format)
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</a

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.

Complement: (b(n)) = (2, 4, 6, 7, 8, 10, 11, 12, 13, 14, 16, ...)

MATHEMATICA

Fold[Append[#1, #1[[-1]] + Complement[Range[Max@#1 + 1], #1][[#2]]] &, {1, 3}, Range[50]] (* Ivan Neretin, Apr 04 2016 *)

CROSSREFS

Cf. A005228 and references therein.

Cf. A293076, A293765, A294381.

Sequence in context: A029518 A061954 A095039 * A025207 A027688 A118403

Adjacent sequences:  A022937 A022938 A022939 * A022941 A022942 A022943

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified November 21 16:27 EST 2017. Contains 295003 sequences.