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

Author

Paul Barry, Jul 18 2003

Keywords

• easy
• nonn
• tabl

Comments

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

Examples

			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.

Formula

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