A145765 Eigentriangle, row sums = A116975, number of compositions of n using terms == (1,4) mod 5.

1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 0, 5, 0, 0, 1, 0, 2, 0, 0, 7, 1, 0, 0, 1, 0, 30, 0, 10, 0, 1, 0, 0, 2, 0, 50, 0, 15, 1, 0, 1, 0, 0, 3, 0, 7, 0, 0, 23, 0, 1, 0, 1, 0, 0, 50, 10, 0, 0, 35, 0, 0, 1, 0, 2, 0, 0, 7, 0, 15, 0, 0, 52, 1, 0, 0, 1, 0, 3, 0, 0, 10, 0, 23, 0

Offset

1,15

Comments

Row sums = A116975, the number of compositions of n using terms == (1,4) mod 5: (1, 1, 1, 2, 3, 5, 7, 10, 15, 23, 35, 52, 77, 115,...). Sum of n-th row terms = rightmost term of next row.

Links

Table of n, a(n) for n=1..100.

Formula

Let T = an infinite lower triangular matrix with (1, 0, 0, 1, 0, 1,...repeat...); (i.e. the characteristic function of (1,4) mod 5) in every column. Let X = an infinite lower triangular matrix with A116975 as the main diagonal prefaced with a 1: (1, 1, 1, 1, 2, 3, 5, 7, 10, 15, 23,...).

Triangle A145765 = T * X.

Example

First few rows of the triangle =
1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 1, 0, 0, 2;
1, 0, 1, 0, 0, 3;
0, 1, 0, 1, 0, 0, 5;
0, 0, 1, 0, 2, 0, 0, 7;
1, 0, 0, 1, 0, 3, 0, 0, 10;
0, 1, 0, 0, 2, 0, 5, 0, 0, 15;
1, 0, 1, 0, 0, 3, 0, 7, 0, 0, 23;
0, 1, 0, 1, 0, 0, 5, 0, 10, 0, 0, 35;
0, 0, 1, 0, 2, 0, 0, 7, 0, 15, 0, 0, 52;
1, 0, 0, 1, 0, 3, 0, 0, 10, 0, 23, 0, 0, 77;
...

Crossrefs

Cf. A145765.

Sequence in context: A356242 A216601 A283000 * A157424 A144961 A144627

Adjacent sequences: A145762 A145763 A145764 * A145766 A145767 A145768

Keyword

eigen,nonn,tabl

Author

Gary W. Adamson, Oct 18 2008

Status

approved