A113722 A variant of Golomb's sequence using odd numbers: a(n) is the number of times 2*n+1 occurs, starting with a(1) = 1.

1, 3, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25, 25, 25, 25, 27

Offset: 0

Author

Floor van Lamoen and Paul D. Hanna, Nov 08 2005

Keywords

• nonn

Comments

a(n) is taken to be the smallest number >= a(n-1) which is compatible with the description.

Examples

			Start with 1 in row 1 and form a triangle where row n is generated from row n-1 by the rule given in the description. Then row 2 will have (1) 3, row 3 will have (3) 5's, row 4 will have (5) 7's, (5) 9's and (5) 11's, etc.
The triangle begins:
1;
3;
5,5,5;
7,7,7,7,7,9,9,9,9,9,11,11,11,11,11; ...
The number of terms in each row (also row sums with offset) is given by A113723: [1,1,3,15,135,3845,769605,3821696361,...].
		

Crossrefs

Cf. A001462 (Golomb's sequence), A113723, A113724, A113676.

Programs

PARI

a=[1,3,5,5,5];for(n=3,20, for(i=1,a[n],a=concat(a,2*n+1)));a