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

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 ...
1 2 5 12 29 ...
1 3 10 34 116 ...
1 4 17 74 325 ...
1 5 26 138 740 ...

Crossrefs

Cf. A016116, A000129, A007052, A086351, A086352.

Sequence in context: A111375 A165997 A046752 * A239830 A140767 A060850

Adjacent sequences: A086347 A086348 A086349 * A086351 A086352 A086353

Keyword

easy,nonn,tabl

Author

Paul Barry, Jul 18 2003

Status

approved