A130049 An inductive sum sequence.

0, 3, 6, 7, 17, 12, 32, 20, 51, 29, 72, 39, 97, 50, 127, 63, 161, 77, 197, 92, 236, 108, 279, 126, 327, 145, 378, 166, 432, 188, 489, 211, 550, 235, 614, 260, 681, 286, 751, 313, 826, 341, 906, 371, 989, 402, 1074, 435, 1162, 469, 1252, 504, 1347, 540, 1445, 577

Offset

1,2

Comments

Complement of A130048. The bisection sequences b(1),b(3),b(5),... and b(2),b(4),b(6),... are strictly increasing, but b(2n)<b(2n-1) for n>=3.

Links

Table of n, a(n) for n=1..56.

Formula

A130049 is the sequence b defined inductively as follows: Let a(1)=1, a(2)=2, b(1)=0, b(2)=3; for n>=3, let x=Floor(n/2) and y=n-x+1. Then a(n)=least positive integer not among a(1),a(2),...,a(n-1), b(1),b(2),...b(n-1) and b(n)=a(1)+a(2)+...+a(x) if n is even, b(n)=a(y)+a(y+1)+...+a(n) if n is odd.

Example

(a(1),a(2),...,a(6))=(1,2,4,5,8,9), so x=4 and b(6)=1+2+4+5=12.
(a(1),a(2),...,a(7))=(1,2,4,5,8,9,10), so y=4 and b(7)=5+8+9+10=32.

Crossrefs

Cf. A130048, A130050, A130051.

Sequence in context: A192124 A334210 A072773 * A333553 A341183 A259256

Adjacent sequences: A130046 A130047 A130048 * A130050 A130051 A130052

Keyword

nonn

Author

Clark Kimberling, May 03 2007

Status

approved