A084346 Triangle read by rows in which row n gives decomposition of Fib(n)*Fib(n+1) into non-adjacent Fibonacci numbers (given by their indices).

2, 3, 5, 2, 7, 3, 9, 5, 2, 11, 7, 3, 13, 9, 5, 2, 15, 11, 7, 3, 17, 13, 9, 5, 2, 19, 15, 11, 7, 3, 21, 17, 13, 9, 5, 2, 23, 19, 15, 11, 7, 3, 25, 21, 17, 13, 9, 5, 2, 27, 23, 19, 15, 11, 7, 3, 29, 25, 21, 17, 13, 9, 5, 2, 31, 27, 23, 19, 15, 11, 7, 3, 33, 29, 25, 21, 17, 13, 9, 5, 2, 35, 31

Offset

1,1

Comments

Read as 2; 3; 5,2; 7,3; 9,5,2; 11,7,3; 13,9,5,2; 15,11,7,3; ... each column is 2,3,5,7,9,11,.. but a new column starts only every other row. Could be read as two interleaved triangular tables: 2, 5,2, 9,5,2, 13,9,5,2, 17,13,9,5,2, 21,17,13,9,5,2 and 3, 7,3, 11,7,3, 15,11,7,3, 19,15,11,7,3, 23,19,15,11,7,3

Links

Table of n, a(n) for n=1..83.

Mathematica

revfibo[0]=0; revfibo[1]=2; revfibo[2]=3; revfibo[3]=4; revfibo[4]=4; revfibo[n_Integer] := Block[{z=Floor@Log[GoldenRatio, Sqrt[5.]n]}, Which[Fibonacci[z+1]<=n, z+1, Fibonacci[z]<=n, z, _, z-1]]; fibodecompose[n_Integer] := revfibo/@(Drop[ #, -1]-Rest[ # ]&[FixedPointList[ #-Fibonacci[revfibo[ # ]]&, n, SameTest->(#2<1&)]]); Table[fibodecompose[Fibonacci[k]Fibonacci[k+1]], {k, 1, 18}]

Crossrefs

Cf. A001654, A077982, A035513.

Sequence in context: A364874 A122556 A175723 * A165911 A354764 A096062

Adjacent sequences: A084343 A084344 A084345 * A084347 A084348 A084349

Keyword

nonn,tabf

Author

Wouter Meeussen, Jun 22 2003

Status

approved