OFFSET
1,13
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Martin Burtscher, Igor Szczyrba, and Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
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).
FORMULA
From Joerg Arndt, Sep 22 2020: (Start)
a(n) = Sum_{k=1..11} a(n-k).
G.f.: x^11/(1 - Sum_{k=1..11} x^k ).
a(n) = 2*a(n-1) - a(n-12). (End)
Another form of the g.f. f: f(z) = (z^(k-1)-z^(k))/(1-2*z+z^(k+1)) with k=11. a(n) = Sum_((-1)^i*binomial(n-10-11*i,i)*2^(n-10-12*i), i=0..floor((n-10)/12))-Sum_((-1)^i*binomial(n-11-11*i,i)*2^(n-11-12*i), i=0..floor((n-11)/12)) with Sum_(alpha(i),i=m..n) = 0 for m>n. - Richard Choulet, Feb 22 2010
MAPLE
a:= proc(n) option remember; `if`(n<11, 0,
`if`(n=11, 1, add(a(n-j), j=1..11)))
end:
seq(a(n), n=1..50); # Alois P. Heinz, Sep 23 2020
MATHEMATICA
With[{nn=11}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vladimir Joseph Stephan Orlovsky, Nov 18 2009
STATUS
approved