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A145765
Eigentriangle, row sums = A116975, number of compositions of n using terms == (1,4) mod 5.
1
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.
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
KEYWORD
eigen,nonn,tabl
AUTHOR
Gary W. Adamson, Oct 18 2008
STATUS
approved