A086352 -id:A086352

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Search: a086352 -id:a086352

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A086350

Square array of Pell related numbers, read by antidiagonals.

+10
3

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

(list; table; graph; refs; listen; history; text; internal format)

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.

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jul 18 2003

STATUS

approved

A086406

Main diagonal of number array A086404.

+10
1

1, 2, 11, 84, 857, 10984, 169803, 3076688, 63968273, 1501465248, 39277112843, 1133193163840, 35748951528681, 1224258310112384, 45233097633685643, 1793524939926112512, 75966131556225961121, 3423203234058532082176

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n)=(n-sqrt(3))^n(1/2-sqrt(3)/6)+(n+sqrt(3))^n(1/2+sqrt(3)/6)

CROSSREFS

Cf. A086352.

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 19 2003

STATUS

approved

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