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A097552
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Number of positive words of length n in the monoid Br_5 of positive braids on 6 strands.
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7
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1, 5, 20, 67, 209, 630, 1873, 5540, 16357, 48265, 142387, 420027, 1239006, 3654820, 10780958, 31801551, 93807834, 276713194, 816245143, 2407749755, 7102350204, 20950424039, 61799299470, 182294802589, 537730934397
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-8,7,-4,1).
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FORMULA
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G.f.: (1 + x^2)^3/(1 - 5*x + 8*x^2 - 7*x^3 + 4*x^4 - x^5). - T. D. Noe, Nov 02 2006
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MATHEMATICA
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LinearRecurrence[{5, -8, 7, -4, 1}, {1, 5, 20, 67, 209, 630, 1873}, 40] (* G. C. Greubel, Apr 19 2021 *)
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PROG
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(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) )); // G. C. Greubel, Apr 19 2021
(Sage)
def A097552_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^2)^3/(1-5*x+8*x^2-7*x^3+4*x^4-x^5) ).list()
A097552_list(40) # G. C. Greubel, Apr 19 2021
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CROSSREFS
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Cf. A097550, A097551, A097553, A097554, A097555, A097556.
Sequence in context: A271066 A271599 A032286 * A322600 A084850 A270169
Adjacent sequences: A097549 A097550 A097551 * A097553 A097554 A097555
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KEYWORD
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nonn,easy
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AUTHOR
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D n Verma, Aug 16 2004
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EXTENSIONS
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Corrected by T. D. Noe, Nov 02 2006
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STATUS
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approved
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