A180264 Triangle, row sums = A006054; derived from an infinite lower triangular matrix with (1,1,1,...) as the leftmost column and (1,2,1,1,1,...) as other columns.

1, 1, 1, 2, 2, 1, 1, 1, 4, 5, 1, 1, 2, 10, 11, 1, 1, 2, 5, 22, 25, 1, 1, 2, 5, 11, 50, 56, 1, 1, 2, 5, 11, 50, 56, 1, 1, 2, 5, 11, 25, 112, 126, 1, 1, 2, 5, 11, 25, 56, 252, 283, 1, 1, 2, 5, 11, 25, 56, 126, 566, 636, 1, 1, 2, 5, 11, 25, 56, 126, 283, 1272, 1429

Offset

1,4

Comments

Row sums = A006054 starting (1, 2, 5, 11, 25, 56, 126,...).

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

Links

Table of n, a(n) for n=1..73.

Formula

Let M = an infinite lower triangular matrix with 1's in the leftmost column,

and (1,2,1,1,1,...) as other columns. Let Q = a diagonalized variant of

A006054 (1, 1, 2, 5, 11, 25, 56,...) as the right border and the rest zeros.

Triangle A180264 = M*Q.

Example

First few rows of the triangle =
.
1;
1, 1;
1, 2, 2;
1, 1, 4, 5;
1, 1, 2, 10, 11;
1, 1, 2, 5, 22, 25;
1, 1, 2, 5, 11, 50, 56;
1, 1, 2, 5, 11, 25, 112, 126;
1, 1, 2, 5, 11, 25, 56, 252, 283;
1, 1, 2, 5, 11, 25, 56, 126, 566, 636;
1, 1, 2, 5, 11, 25, 56, 126, 283, 1272, 1429;
1, 1, 2, 5, 11, 25, 56, 126, 283, 636, 2858, 3211;
...
Example: Row 4 = (1, 1, 4, 5) = termwise products of (1, 1, 2, 1) and (1, 1, 2, 5).

Crossrefs

Cf. A006054

Sequence in context: A350818 A340142 A242618 * A225200 A128706 A375970

Adjacent sequences: A180261 A180262 A180263 * A180265 A180266 A180267

Keyword

nonn,tabf

Author

Gary W. Adamson, Aug 21 2010

Status

approved