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A175011 Triangle read by rows, antidiagonals of an array generated from INVERT transforms of variants of (1, 2, 3,...). 2
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 (list; table; graph; refs; listen; history; text; internal format)
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: A245841 A011404 A002211 * A211700 A171840 A132309

Adjacent sequences:  A175008 A175009 A175010 * A175012 A175013 A175014

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Apr 03 2010

STATUS

approved

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Last modified October 15 15:48 EDT 2018. Contains 316236 sequences. (Running on oeis4.)