A207539 Dodecanacci numbers (12th-order Fibonacci sequence): a(n) = a(n-1) +...+ a(n-12) with a(0)=...=a(11)=1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 23, 45, 89, 177, 353, 705, 1409, 2817, 5633, 11265, 22529, 45057, 90102, 180181, 360317, 720545, 1440913, 2881473, 5762241, 11523073, 23043329, 46081025, 92150785, 184279041, 368513025, 736935948, 1473691715

Offset: 0

Author

Michael Burkhart, Feb 18 2012

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Kai Wang, Identities for generalized enneanacci numbers, Generalized Fibonacci Sequences (2020).
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1,1,1,1).

Crossrefs

Cf. A000045, A000213, A000288, A127624, A168083.

Programs

Maple

f12:=proc(n) option remember: if n<=12 then 1: else add(f12(n-i),i=1..12): fi: end:

Mathematica

LinearRecurrence[Table[1, {12}], Table[1, {12}], 100]

PARI

x='x+O('x^50); Vec((1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11 +10*x^12)/(1-2*x+x^13)) \\ G. C. Greubel, Jul 28 2017

Formula

G.f.: (1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9-x^10-x^11 +10*x^12)/(1 -2*x +x^13).