A144962 Eigentriangle, row sums = A000084

1, 1, 1, 1, 1, 2, 3, 1, 2, 4, 5, 3, 2, 4, 10, 17, 5, 6, 4, 10, 24, 41, 17, 10, 12, 10, 24, 66, 127, 41, 34, 20, 30, 24, 66, 180, 365, 127, 82, 68, 50, 72, 66, 180, 522, 1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532

Offset

1,6

Comments

Row sums = A000084: (1, 2, 4, 10, 24, 66,...).

Right border = A000084 shifted: (1, 1, 2, 4, 10, 24,...)

Left border = A001572: (1, 1, 1, 3, 5, 17, 41,...).

A000084 = the INVERT transform of A001572.

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

Links

Table of n, a(n) for n=1..55.

Formula

Triangle read by rows, T(n,k) = A001572(n-k+1) * (A000084 * 0^(n-k)), 1<=k<=n.

Given an A001572 "decrescendo" triangle: (1; 1,1; 1,1,1; 3,1,1,1; 5,3,1,1,1;...), where A001572 begins: (1, 1, 1, 3, 5, 17, 41, 127,...); apply termwise products of the decrescendo triangle row terms to A000084 terms: (1, 2, 4, 10, 24, 66, 180, 522,...).

Example

First few rows of the triangle =
1;
1, 1;
1, 1, 2;
3, 1, 2, 4;
5, 3, 2, 4, 10;
17, 5, 6, 4, 10, 24;
41, 17, 10, 12, 10, 24, 66;
127, 41, 34, 20, 30, 24, 66, 180;
365, 127, 82, 68, 50, 72, 66, 180, 522;
1119, 365, 254, 164, 170, 120, 198, 180, 522, 1532;
...
Example: row 5 = (5, 3, 2, 4, 10) = termwise products of (5, 3, 1, 1, 1) and (1, 1, 2, 4, 10).

Crossrefs

A000084, Cf. A001572

Sequence in context: A341826 A257669 A181803 * A227542 A338900 A244567

Adjacent sequences: A144959 A144960 A144961 * A144963 A144964 A144965

Keyword

nonn,tabl

Author

Gary W. Adamson, Sep 27 2008

Status

approved