A167269 Triangle read by rows, Pascal's triangle columns interleaved with 1's.

1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 3, 1, 1, 5, 1, 6, 1, 1, 1, 6, 1, 10, 1, 4, 1, 1, 7, 1, 15, 1, 10, 1, 1, 1, 8, 1, 21, 1, 20, 1, 5, 1, 1, 9, 1, 28, 1, 35, 1, 15, 1, 1, 1, 10, 1, 36, 1, 56, 1, 35, 1, 6, 1, 1, 11, 1, 45, 1, 84, 1, 70, 1, 21, 1, 1, 1, 12, 1, 55, 1, 120, 1, 126, 1, 56, 1, 7, 1

Offset

0,5

Comments

Row sums, A167270: (1, 2, 4, 6, 10, 15, 24, 37,...) tend to phi, 1.618...;

e.g. 2592/1604 = 1.61596...

Links

Table of n, a(n) for n=0..90.

Formula

Given Pascal's triangle columns >0, insert 1's as alternate columns.

Example

First few rows of the triangle =
1;
1, 1;
1, 2, 1;
1, 3, 1, 1;
1, 4, 1, 3, 1;
1, 5, 1, 6, 1, 1;
1, 6, 1, 10, 1, 4, 1;
1, 7, 1, 15, 1, 10, 1, 1;
1, 8, 1, 21, 1, 20, 1, 5, 1;
1, 9, 1, 28, 1, 35, 1, 15, 1, 1;
1, 10, 1, 36, 1, 56, 1, 35, 1, 6, 1;
1, 11, 1, 45, 1, 84, 1, 70, 1, 21, 1, 1;
1, 12, 1, 55, 1, 120, 1, 126, 1, 56, 1, 7, 1;
1, 13, 1, 66, 1, 165, 1, 210, 1, 126, 1, 28, 1, 1;
1, 14, 1, 78, 1, 220, 1, 330, 1, 252, 1, 84, 1, 8, 1;
1, 15, 1, 91, 1, 286, 1, 495, 1, 462, 1, 210, 1, 36, 1, 1;
1, 16, 1, 105, 1, 364, 1, 715, 1, 792, 1, 461, 1, 120, 1, 9, 1;
...

Crossrefs

A167270

Sequence in context: A165430 A334215 A164823 * A105535 A182980 A244051

Adjacent sequences: A167266 A167267 A167268 * A167270 A167271 A167272

Keyword

nonn,tabl

Author

Gary W. Adamson & Mats Granvik, Oct 31 2009

Status

approved