A221131 Table, T, read by antidiagonals where T(-j,k) = ((1+sqrt(j))^k + (1-sqrt(j))^k)/2.

1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, -1, -2, 1, 1, 1, -2, -5, -4, 1, 1, 1, -3, -8, -7, -4, 1, 1, 1, -4, -11, -8, 1, 0, 1, 1, 1, -5, -14, -7, 16, 23, 8, 1, 1, 1, -6, -17, -4, 41, 64, 43, 16, 1, 1, 1, -7, -20, 1, 76, 117, 64, 17, 16, 1, 1, 1, -8, -23, 8, 121, 176, 29, -128, -95, 0, 1

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com) and Robert G. Wilson v, Jan 02 2013

Keywords

• sign
• tabl

Comments

.j\k.........0..1...2....3...4....5....6......7.......8......9......10

.0: A000012..1..1...1....1...1....1....1......1.......1......1.......1

-1: A146559..1..1...0...-2..-4...-4....0......8......16.....16.......0

-2: A087455..1..1..-1...-5..-7....1...23.....43......17....-95....-241

-3: A138230..1..1..-2...-8..-8...16...64.....64....-128...-512....-512

-4: A006495..1..1..-3..-11..-7...41..117.....29....-527..-1199.....237

-5: A138229..1..1..-4..-14..-4...76..176...-104...-1264..-1904....3776

-6: A090592..1..1..-5..-17...1..121..235...-377...-2399..-2159...12475

-7: A090590..1..1..-6..-20...8..176..288...-832...-3968..-1280...29184

-8: A025172..1..1..-7..-23..17..241..329..-1511...-5983...1633...57113

-9: A120743..1..1..-8..-26..28..316..352..-2456...-8432...7696...99712

-10: ........1..1..-9..-29..41..401..351..-3709..-11279..18241..160551

Crossrefs

Cf. A084097,

Rows: A000012, A146559, A087455, A138230, A006495, A138229, A090592, A090590, A025172, A120743.

Columns: A000012, A000012, A024000, 1-3n, A028884, A134593.

Programs

Mathematica

T[j_, k_] := Expand[((1 + Sqrt[j])^k + (1 - Sqrt[j])^k)/2]; Table[ T[ -j + k, k], {j, 0, 11}, {k, 0, j}] // Flatten