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
Examples
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
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+2,n) = A000285(n).
T(n+4,n) = A021120(n).
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+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).