A144029 Eigentriangle by rows, A055615(n-k+1)*A144028(k-1); 1<=k<=n.

1, -2, 1, -3, -2, -1, 0, -3, 2, -6, -5, 0, 3, 12, -7, 6, -5, 0, 18, 14, 3, -7, 6, 5, 0, 21, -6, 36, 0, -7, -6, 30, 0, -9, -72, 55, 0, 0, 7, -36, 35, 0, -108, -110, -9, 10, 0, 0, 42, -42, -15, 0, -165, 18, -221, -11, 10, 0, 0, 49, 18, -180, 0, 27, 442, -373, 0, -11, -10, 0, 0, -21, 216, -275, 0, 663, 746, -18

Offset

1,2

Comments

Row sums = A144028. Right border = A144028 shifted.

Left border = A055615, n*mu(n).

Sum of n-th row terms = rightmost term of next row.

Links

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

Formula

Eigentriangle by rows, A055615(n-k+1)*A144028(k-1); 1<=k<=n.

Example

First few rows of the triangle =
1;
-2, 1;
-3, -2, -1;
0, -3, 2, -6;
-5, 0, 3, 12, -7;
6, -5, 0, 18, 14, 3;
-7, 6, 5, 0, 21, -6, 36;
0, -7, -6, 30, 0, -9, -72, 55;
0, 0, 7, -36, 35, 0, -108, -110, -9;
10, 0, 0, 42, -42, -15, 0, -165, 18, -221;
...
Row 4 = (0, -3, 2, -6) = termwise products of (0, -3, -2, 1) and (1, 1, -1, -6) = (0*1, -3*1, -2*-1, 1*(-6)). (0, -3, -2, 1) = the first 4 terms of A055615, n*mu(n), reversed.
(1, 1, -1, 6) = the first 4 terms A144028, shifted.

Maple

read("transforms");
A055615 := proc(n) n*numtheory[mobius](n) ; end proc:
A144028 :=proc(n) if n = 0 then 1; else L := [seq(A055615(i), i=1..n+2)] ; INVERT(L) ; op(n, %) ; end if; end proc:
A144029 := proc(n, k) A055615(n-k+1)*A144028(k-1) ; end proc: # R. J. Mathar, Jan 27 2011

Crossrefs

Cf. A055615, A144028.

Sequence in context: A190451 A282743 A191360 * A347030 A166949 A114890

Adjacent sequences: A144026 A144027 A144028 * A144030 A144031 A144032

Keyword

tabl,sign

Author

Gary W. Adamson, Sep 07 2008

Extensions

Entries corrected starting from row 10. - R. J. Mathar, Jan 27 2011

Status

approved