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A168083 Fibonacci 12-step numbers. 6
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4095, 8189, 16376, 32748, 65488, 130960, 261888, 523712, 1047296, 2094336, 4188160, 8375296, 16748544, 33492993, 66977797, 133939218, 267845688, 535625888, 1071120816 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,14

COMMENTS

From Ruediger Jehn, Nov 30 2020: (Start)

a(n+12) is the number of compositions of n with no part greater than 12.

a(n+12) is the number of ways of throwing n with an unstated number of dodecahedra (here dice with numbers from 1 to 12).

(End)

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 (1,1,1,1,1,1,1,1,1,1,1,1).

FORMULA

Another form of the g.f. f: f(z)= (z^(k-1)-z^(k))/(1-2*z+z^(k+1)) with k=12. 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=12 and convention sum(alpha(i),i=m..n)=0 for m>n. - Richard Choulet, Feb 22 2010

MAPLE

k:=12: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); 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); # Richard Choulet, Feb 22 2010

MATHEMATICA

a={1, 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}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, 50]

With[{nn=12}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *)

CROSSREFS

Sequence in context: A271482 A335890 A219531 * A221180 A219615 A168084

Adjacent sequences:  A168080 A168081 A168082 * A168084 A168085 A168086

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Nov 18 2009

STATUS

approved

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)