A237452 Zero-based row index to irregular tables organized as successively larger square matrices.

0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5

Offset

1,12

Comments

With sequences constructed of successively larger kxk square matrices (cf. A074279), a(n) will return the distance of n from the top edge of the matrix that n is located in, with 0 standing for the topmost row in that matrix (please see the Example section).

A237451 gives the corresponding column index.

A238013 and A121997 give these same row and column indices, but starting the numbering with index 1. - M. F. Hasler, Feb 17 2014

Links

Antti Karttunen, Table of squares with sizes 1x1 .. 30x30, flattened

Formula

a(n) = floor((A064866(n)-1)/A074279(n)).

a(n) = A238013(n)-1. - M. F. Hasler, Feb 16 2014

Example

This irregular table begins as:
0;
0,0;
1,1;
0,0,0;
1,1,1;
2,2,2;
0,0,0,0;
1,1,1,1;
2,2,2,2;
3,3,3,3;
0,0,0,0,0;
1,1,1,1,1;
2,2,2,2,2;
3,3,3,3,3;
4,4,4,4,4;
...

Prog

(Scheme) (define (A237452 n) (floor->exact (/ (-1+ (A064866 n)) (A074279 n))))

Crossrefs

Cf. A064866, A074279, A237451, A237265, A238013 and A121997.

Sequence in context: A308583 A093315 A204267 * A132784 A180834 A214458

Adjacent sequences: A237449 A237450 A237451 * A237453 A237454 A237455

Keyword

nonn,tabf

Author

Antti Karttunen, Feb 08 2014

Status

approved