

A117918


Difference row triangle of the Pell sequence.


4



1, 1, 2, 2, 3, 5, 2, 4, 7, 12, 4, 6, 10, 17, 29, 4, 8, 14, 24, 41, 70, 8, 12, 20, 34, 58, 99, 169, 8, 16, 28, 48, 82, 140, 239, 408, 16, 24, 40, 68, 116, 198, 338, 577, 985, 16, 32, 56, 96, 164, 280, 478, 816, 1393, 2378, 32, 48, 80, 136, 232, 396, 676, 1154, 1970, 3363, 5741
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OFFSET

1,3


COMMENTS

Leftmost column (1, 1, 2, 2, 4, 4,...), (A016116); is the inverse binomial transform of the Pell sequence.


REFERENCES

Raymond Lebois, "Le theoreme de Pythagore et ses implications", p. 123, Editions PIM, (1979).


LINKS

Table of n, a(n) for n=1..66.


FORMULA

Difference rows of the Pell sequence A000129 starting (1, 2, 5, 12...) become the diagonals of the triangle A117918.


EXAMPLE

Right border = the Pell sequence. First difference row (1, 3, 7, 17, 41...) is the next diagonal.
First few rows of the triangle are:
1;
1, 2;
2, 3, 5;
2, 4, 7, 12;
4, 6, 10, 17, 29;
4, 8, 14, 24, 41, 70;
8, 12, 20, 34, 58, 99, 169;
...


CROSSREFS

Cf. A000129, A016116.
Sequence in context: A175908 A152430 A297495 * A302495 A185688 A203955
Adjacent sequences: A117915 A117916 A117917 * A117919 A117920 A117921


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Apr 02 2006


STATUS

approved



