A159906 Triangle read by rows, A126988 * A054533

1, 1, 1, 2, -1, 2, 2, 0, 0, 2, 4, -1, -1, -1, 4, 2, 0, 2, -1, 1, 2, 6, -1, -1, -1, -1, -1, 6, 4, 0, 0, 0, 0, 0, 0, 4, 6, -3, 3, 0, 0, -3, 0, 0, 6, 4, 2, -1, -3, 4, -1, 1, -1, 1, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 4, -4, 4, 2, 2, 0, 0, -2, 0, 2, 0, 4

Offset

1,4

Comments

Row sums = n, right and left borders = A000012, phi(n).

Links

Table of n, a(n) for n=1..78.

Formula

Triangle read by rows, A126988 * A054533, where A054533 = the lower half of the Ramanujan sum table.

Example

First few rows of the triangle =
1;
1,...1;
2,..-1,...2;
2,...0,...0,...2;
4,..-1,..-1,..-1,...4;
2,...0,...2,..-1,...1,...2;
6,..-1,..-1,..-1,..-1,..-1,...6;
4,...0,...0,...0,...0,...0,...0,...4;
6,..-3,...3,...0,...0,..-3,...0,...0,...6;
4,...2,..-1,..-3,...4,..-1,...1,..-1,...1,...4;
10,.-1,..-1,..-1,..-1,..-1,..-1,..-1,..-1,..-1,...10;
4,..-4,...4,...2,...2,...0,...0,..-2,...0,...2,....0,...4;
12,.-1,..-1,..-1,..-1,..-1,..-1,..-1,..-1,..-1,...-1,..-1,...12;
6,...4,..-1,..-3,..-1,..-3,...6,..-1,...1,..-1,....1,...1,....1,...6;
8,..-7,...5,..-2,...8,..-2,...1,...1,..-2,..-4,....1,..-2,....1,...1,...8;
8,...0,...0,...0,...0,...0,...0,...0,...0,...0,....0,...0,....0,...0,...0,...8;
...

Crossrefs

Cf. A054533, A126988.

Sequence in context: A286129 A230322 A174950 * A263444 A276321 A152196

Adjacent sequences: A159903 A159904 A159905 * A159907 A159908 A159909

Keyword

tabl,sign

Author

Gary W. Adamson, Apr 25 2009

Extensions

a(29) split and more terms from Georg Fischer, May 29 2023

Status

approved