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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 (list; graph; refs; listen; history; text; internal format)
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, ...). n-th 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

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)