A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3, ...).

1, 1, 2, 1, 2, 5, 1, 2, 2, 16, 1, 2, 2, 5, 45, 1, 2, 2, 2, 12, 125, 1, 2, 2, 2, 5, 24, 341, 1, 2, 2, 2, 2, 12, 48, 918, 1, 2, 2, 2, 2, 7, 18, 97, 2453, 1, 2, 2, 2, 2, 2, 16, 28, 195, 6515

Offset

1,3

Comments

Row sums = A001906, the even-indexed Fibonacci numbers starting (1, 3, 8, 21, ...).

Links

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

Formula

Given S(x) = (1 + 2x + 3x^2 + ...), where (1, 2, 3, ...) = the INVERTi transform of (1, 3, 8, 21, 55, ...); k-th row of the array = INVERT transform of S(x^k). Take finite differences of array columns starting from the topmost "1"; becoming rows of the triangle.

Example

First few rows of the array:
  1, 3, 8, 21, 55, 144, 377, 987, 2584, ...
  1, 1, 3,  5, 10,  19,  36,  69,  131, ...
  1, 1, 1,  3,  5,   7,  12,  21,   34, ...
  1, 1, 1,  1,  3,   5,   7,   9,   16, ...
  1, 1, 1,  1,  1,   3,   5,   7,    9, ...
  1, 1, 1,  1,  1,   1,   3,   5,    7, ...
  ...
Taking finite differences from the bottom to top starting with the last "1" we obtain triangle A175011:
  1;
  1, 2;
  1, 2, 5;
  1, 2, 2, 16;
  1, 2, 2,  5, 45;
  1, 2, 2,  2, 12, 125;
  1, 2, 2,  2,  5,  24, 341;
  1, 2, 2,  2,  2,  12,  48, 918;
  1, 2, 2,  2,  2,   7,  18,  97, 2453;
  1, 2, 2,  2,  2,   2,  16,  28,  195, 6515;
  ...

Crossrefs

Cf. A001906.

Sequence in context: A011404 A002211 A308947 * A211700 A171840 A132309

Adjacent sequences: A175008 A175009 A175010 * A175012 A175013 A175014

Keyword

nonn,tabl

Author

Gary W. Adamson, Apr 03 2010

Status

approved