

A117584


Generalized Pellian triangle.


2



1, 1, 2, 1, 3, 5, 1, 4, 7, 12, 1, 5, 9, 17, 29, 1, 6, 11, 22, 41, 70, 1, 7, 13, 27, 53, 99, 169, 1, 8, 15, 32, 65, 128, 239, 408, 1, 9, 17, 37, 77, 157, 309, 577, 985, 1, 10, 19, 42, 89, 186, 379, 746, 1393, 2378
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OFFSET

1,3


COMMENTS

Diagonals of the triangle are composed of the infinite set of Pellian sequences. Right border = A000129. Next diagonal going to the left = A001333 starting (1, 3, 7, 17, ...). A048654 = (1, 4, 9, ...). A048655 = (1, 5, 11, ...). A048693 = (1, 6, 13, ...); and so on.


LINKS

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


FORMULA

Antidiagonals of the generalized Pellian array. First row of the array = A000129: (1, 2, 5, 12, ...). nth row of the array starts (1, n+1, ...); as a Pellian sequence.


EXAMPLE

First few rows of the triangle are:
1;
1, 2;
1, 3, 5;
1, 4, 7, 12;
1, 5, 9, 17, 29;
1, 6, 11, 22, 41, 70;
1, 7, 13, 27, 53, 99, 169;
...
The triangle rows are antidiagonals of the generalized Pellian array:
1, 2, 5, 12, 29, ...
1, 3, 7, 17, 41, ...
1, 4, 9, 22, 53, ...
1, 5, 11, 27, 65, ...
...
For example, in the row (1, 5, 11, 27, 65, ...), 65 = 2*27 + 11.


CROSSREFS

Cf. A000129, A001333, A048654, A048655, A048693.
Sequence in context: A093412 A119355 A076110 * A199847 A047997 A188211
Adjacent sequences: A117581 A117582 A117583 * A117585 A117586 A117587


KEYWORD

nonn


AUTHOR

Gary W. Adamson, Mar 29 2006


STATUS

approved



