A086350 - OEIS

A086350

Square array of Pell related numbers, read by antidiagonals.

1, 1, 1, 1, 2, 2, 1, 3, 5, 2, 1, 4, 10, 12, 4, 1, 5, 17, 34, 29, 4, 1, 6, 26, 74, 116, 70, 8, 1, 7, 37, 138, 325, 396, 169, 8, 1, 8, 50, 232, 740, 1432, 1352, 408, 16, 1, 9, 65, 362, 1469, 3988, 6317, 4616, 985, 16, 1, 10, 82, 534, 2644, 9354, 21544, 27878, 15760, 2378, 32

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OFFSET

0,5

COMMENTS

Rows include A016116, A000129, A007052, A086351. Main diagonal is A086352. Rows are successive binomial transforms of (1, 1, 2, 2, 4, 4, ...).

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n, k) = ((1+sqrt(2))(k+sqrt(2))^n-(1-sqrt(2))(k-sqrt(2))^n)/(sqrt(8)).

EXAMPLE

Rows start

1 1 2 2 4 ...