A137710 - OEIS

A137710

Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); left border = (1, 2, 4, 8, 16, 32, ...).

1, 2, 1, 4, 1, 1, 8, 2, 1, 1, 16, 4, 2, 1, 1, 32, 8, 3, 2, 1, 1, 64, 16, 6, 2, 2, 1, 1, 64, 16, 6, 2, 2, 1, 1, 128, 32, 12, 5, 2, 2, 1, 1, 256, 64, 24, 10, 4, 2, 2, 1, 1, 512, 128, 48, 21, 9, 4, 2, 2, 1, 1, 1024, 256, 96, 42, 19, 18, 4, 2, 2, 1, 1, 2048, 512, 192, 84, 40, 18, 18, 4, 2, 2, 1, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Row sums = A137711: (1, 3, 6, 12, 24, 47, 92, 183, ...).

Eigensequence of the triangle = even-indexed Fibonacci numbers starting (1, 3, 8, 21, 55, ...). Cf. triangle A180339. - Gary W. Adamson, Aug 28 2010

LINKS

Table of n, a(n) for n=1..85.

FORMULA

The triangle is generated by two rules: T(n,k) = T(n-1, k-1) - T(n-k, k-1); and left border = 1, 2, 4, 8, 16, ...

EXAMPLE

First few rows of the triangle: