A217762 Square array T, read by antidiagonals: T(n,k) = F(n) + 2*F(k) where F(n) is the n-th Fibonacci number.

0, 2, 1, 2, 3, 1, 4, 3, 3, 2, 6, 5, 3, 4, 3, 10, 7, 5, 4, 5, 5, 16, 11, 7, 6, 5, 7, 8, 26, 17, 11, 8, 7, 7, 10, 13, 42, 27, 17, 12, 9, 9, 10, 15, 21, 68, 43, 27, 18, 13, 11, 12, 15, 23, 34, 110, 69, 43, 28, 19, 15, 14, 17, 23, 36, 55, 178, 111, 69, 44, 29, 21

Offset

0,2

Links

Table of n, a(n) for n=0..71.

Formula

T(n,0) = A000045(n).

T(1,k) = A001588(k).

T(n,1) = T(n,2) = A157725(n).

T(n,3) = A157727(n).

T(n,n)= A022086(n) = 3*A000045(n).

T(n+1,n) = A000032(n+1) = A000204(n+1).

T(n+2,n) = A000285(n).

T(n+3,n) = A013655(n+1) = A001060(n+1).

T(n+4,n) = A021120(n).

T(n+5,n) = A022088(n+2) = 5*A000045(n+2).

T(n+6,n) = A022097(n+2).

T(n+7,n) = A022122(n+2).

T(n+8,n) = 3*A013655(n+2).

T(n+9,n) = A097657(n+2).

T(n+10,n) = A022118(n+4).

T(n,n+1) = A000045(n+3).

T(n,n+2) = A013655(n+1) = A001060(n+1).

T(n,n+3) = A000032(n+3).

T(n,n+4) = A022095(n+2).

T(n,n+5) = A022120(n+2).

T(n,n+6) = A022136(n+2).

T(n,n+7) = A022098(n+4).

T(n,n+8) = A022380(n+4).

T(n,n+9) = A206419(n+6).

Sum(T(n-k,k), 0<=k<=n) = 3*A000071(n+2).

Example

Square array begins:
...0....2....2....4....6...10...16...26...42...
...1....3....3....5....7...11...17...27...43...
...1....3....3....5....7...11...17...27...43...
...2....4....4....6....8...12...18...28...44...
...3....5....5....7....9...13...19...29...45...
...5....7....7....9...11...15...21...31...47...
...8...10...10...12...14...18...24...34...50...
..13...15...15...17...19...23...29...39...55...
..21...23...23...25...27...31...37...47...63...
..34...36...36...38...40...44...50...60...76...
..55...57...57...59...61...65...71...81...97...
..89...91...91...93...95...99..105..115..131...
.144..146..146..148..150..154..160..170..186...
...

Crossrefs

Cf. A000045

Sequence in context: A132163 A355079 A205682 * A172467 A110582 A162507

Adjacent sequences: A217759 A217760 A217761 * A217763 A217764 A217765

Keyword

nonn,tabl

Author

Philippe Deléham, Apr 07 2013

Status

approved