A144106 Eigentriangle, row sums = (2n + 1).

1, 2, 1, 0, 2, 3, -4, 0, 6, 5, -4, -4, 0, 10, 7, 4, -4, 12, 0, 14, 9, 12, 4, -12, -20, 0, 18, 11, 4, 12, 12, -20, -28, 0, 22, 13, -20, 4, 36, 20, -28, -36, 0, 26, 15, -28, -20, 12, 60, 28, -36, -44, 0, 30, 17

Offset

0,2

Comments

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

Links

Table of n, a(n) for n=0..54.

Formula

Eigentriangle by rows, T(n,k) = A078050(n-k) * X; where X = an infinite lower triangular matrix with (1, 1, 3, 5, 7, 9,...) in the main diagonal and the rest zeros. A078050 is signed: (1, 2, 0, -4, -4, 4, 12, 4, -20, -28,...) = the INVERTi transform of the odd numbers: (1, 3, 5, 7,...).

Example

First few rows of the triangle =
1;
2, 1;
0, 2, 3;
-4, 0, 6, 5;
-4, -4, 0, 10, 7;
4, -4, -12, 0, 14, 9;
12, 4, -12, -20, 0, 18, 11;
4, 12, 12, -20, -28, 0, 22, 13;
-20, 4, 36, 20, -28, -36, 0, 26, 15;
...
Row 3 = (-4, 0, 6, 5) = (-4*1, 0*1, 3*2, 5*1) = termwise product of (-4, 0, 2, 1) and (1, 1, 3, 5); where (-4, 0, 2, 1) = the first 4 terms of signed A078050 (reversed).

Crossrefs

Cf. A005408, A078050.

Sequence in context: A296529 A110280 A061009 * A104558 A206022 A115247

Adjacent sequences: A144103 A144104 A144105 * A144107 A144108 A144109

Keyword

tabl,sign

Author

Gary W. Adamson, Sep 11 2008

Status

approved