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 A168084 Fibonacci 13-step numbers. 5
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8191, 16381, 32760, 65516, 131024, 262032, 524032, 1048000, 2095872, 4191488, 8382464, 16763904, 33525760, 67047424, 134086657, 268156933, 536281106, 1072496696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, J. Int. Seq. 18 (2015) # 15.4.7. Index entries for linear recurrences with constant coefficients, signature (1, 1, 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=13. then a(n)=sum((-1)^i*binomial(n-k+1-k*i,i)*2^(n-k+1-(k+1)*i),i=0..floor((n-k+1)/(k+1)))-sum((-1)^i*binomial(n-k-k*i,i)*2^(n-k-(k+1)*i),i=0..floor((n-k)/(k+1))) with k=13 and convention sum(alpha(i),i=m..n)=0 for m>n. - Richard Choulet, Feb 22 2010 MAPLE k:=13:a:=taylor((z^(k-1)-z^(k))/(1-2*z+z^(k+1)), z=0, 51); for p from 0 to 50 do j(p):=coeff(a, z, p):od :seq(j(p), p=0..50); k:=13:for n from 0 to 50 do l(n):=sum((-1)^i*binomial(n-k+1-k*i, i)*2^(n-k+1-(k+1)*i), i=0..floor((n-k+1)/(k+1)))-sum((-1)^i*binomial(n-k-k*i, i)*2^(n-k-(k+1)*i), i=0..floor((n-k)/(k+1))):od:seq(l(n), n=0..50); # Richard Choulet, Feb 22 2010 MATHEMATICA a={1, 0, 0, 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, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, 50] With[{nn=13}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *) CROSSREFS Cf. A000078, A001591, A001592, A122189, A079262, A168083. Sequence in context: A168083 A221180 A219615 * A133025 A216095 A190126 Adjacent sequences:  A168081 A168082 A168083 * A168085 A168086 A168087 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Nov 18 2009 STATUS approved

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Last modified October 14 14:26 EDT 2019. Contains 328018 sequences. (Running on oeis4.)