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A168082 Fibonacci 11-step numbers. 3
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2047, 4093, 8184, 16364, 32720, 65424, 130816, 261568, 523008, 1045760, 2091008, 4180992, 8359937, 16715781, 33423378, 66830392, 133628064, 267190704, 534250592, 1068239616 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,13

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1).

FORMULA

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

for n from 0 to 50 do l(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)):od:seq(l(n), n=0..50); a:=taylor((z^(10)-z^(11))/(1-2*z+z^(12)), z=0, 51); for p from 0 to 50 do j(p):=coeff(a, z, p):od :seq(j(p), p=0..50); # Richard Choulet, Feb 22 2010

MATHEMATICA

a={1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; Flatten[Prepend[Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 60}], Table[0, {m, Length[a]-1}]]]

LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, 50] (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *)

With[{nn=11}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *)

CROSSREFS

Sequence in context: A145117 A172320 A234592 * A295081 A227843 A271482

Adjacent sequences:  A168079 A168080 A168081 * A168083 A168084 A168085

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Nov 18 2009

STATUS

approved

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Last modified February 20 16:36 EST 2020. Contains 332080 sequences. (Running on oeis4.)