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Search: id:A122762
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| A122762 |
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a(0) = ... = a(9) = 1; for n >= 10, a(n) = a(n - 2) + a(n - 4) + a(n - 5) + a(n - 7) + a(n - 8) + a(n - 10). |
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1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 11, 11, 21, 26, 41, 56, 86, 121, 181, 256, 381, 541, 801, 1146, 1686, 2426, 3551, 5131, 7486, 10841, 15791, 22896, 33321, 48346, 70321, 102076, 148416, 215506, 313256, 454961, 661206, 960446, 1395686, 2027501
(list; graph; listen)
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OFFSET
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0,11
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COMMENT
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Shannon mentions this recurrence with characteristic polynomial x^10+x^8+x^7+x^5+x^4+x^2-1==0 in connection with the channel capacity Cp=Log[W]=Log[xroot_max]=0.539...
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REFERENCES
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Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, p37-38
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FORMULA
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O.g.f.: (-1-x+x^4+2*x^5+2*x^6+3*x^7+4*x^8+4*x^9)/(-1+x^2+x^4+x^5+x^7+x^8+x^10). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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MATHEMATICA
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a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[6] = 1; a[7] = 1; a[8] = 1; a[9] = 1; a[n_] := a[n] = a[n - 2] + a[n - 4] + a[n - 5] + a[n - 7] + a[n - 8] + a[n - 10] Table[a[n], {n, 0, 100}]
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CROSSREFS
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Adjacent sequences: A122759 A122760 A122761 this_sequence A122763 A122764 A122765
Sequence in context: A021603 A065480 A096474 this_sequence A046605 A095899 A109538
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 21 2006
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EXTENSIONS
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Edited by njas, May 09 2007
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