A220469 Fibonacci 14-step numbers, a(n) = a(n-1) + a(n-2) + ... + a(n-14).

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16383, 32765, 65528, 131052, 262096, 524176, 1048320, 2096576, 4193024, 8385792, 16771072, 33541120, 67080192, 134156288, 268304384, 536592385, 1073152005, 2146238482, 4292345912, 8584429728

Offset: 1

Author

Ruskin Harding, Feb 20 2013

Keywords

• nonn

Comments

Also called tetradecanacci numbers. In previous similar sequences, a(1),...,a(n-1) have been set equal to zero and a(n)=1. For example, A168084 (Fibonacci 13-step numbers) has 12 0's as the first 12 terms and a(13)=1.

Links

• M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7
• Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1).

Crossrefs

Cf. A000045 (Fibonacci), A000073 (tribonacci), A000078 (tetranacci), A001591 (pentanacci).

Programs

Mathematica

FibonacciSequence[n_, kMax_] := Module[{a, s}, a = Join[{1}, Table[0, {n - 1}]]; lst = {}; Table[s = Plus @@ a; a = RotateLeft[a]; a[[n]] = s, {k, 1, kMax}]]; FibonacciSequence[14, 50] (* T. D. Noe, Feb 20 2013 *)
Drop[LinearRecurrence[PadRight[{},14,1],Join[PadRight[{},13,0],{1}],50],13] (* Harvey P. Dale, Feb 25 2013 *)
LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1},{1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096},35] (* Ray Chandler, Aug 03 2015 *)