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Search: id:A104144
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| A104144 |
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a(n) = a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8)+a(n-9). |
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+0
4
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| 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144, 16272, 32512, 64960, 129792, 259328, 518145, 1035269, 2068498, 4132920, 8257696, 16499120, 32965728, 65866496, 131603200, 262947072, 525375999, 1049716729, 2097364960
(list; graph; listen)
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OFFSET
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0,11
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COMMENT
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Fibonacci 9-step numbers.
For n >= 8, this gives the number of integers written without 0 in base ten, the sum of digits of which is equal to n-7. E.g. a(11)=8 because we have the 8 numbers : 4, 13, 22, 31, 112, 121, 211, 1111.
The offset for this sequence is fairly arbitrary. - N. J. A. Sloane (njas(AT)research.att.com).
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..208
Eric Weisstein's World of Mathematics, Fibonacci n-Step Number
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FORMULA
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a(n)=sum_{k=1..9} a(n-k) for n>8, a(8)=1, a(n)=0 for n=0..7
a(1-10)=1,1,2,4,8,16,32,64,128,256. a(11 & following)=127*2^(n-9)+(.5+sqrt1.25)^(n-7)/sqrt5-(.5-sqrt1.25)^(n-7)/sqrt5. Offset 11. a(11)=511. [From Al Hakanson (hawkuu(AT)gmail.com), Feb 14 2009]
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MATHEMATICA
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a={1, 0, 0, 0, 0, 0, 0, 0, 0}; Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 50}]
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CROSSREFS
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Cf. A000045, A000073, A000078, A001591, A001592, A066178, A079262 (Fibonacci n-step numbers).
Sequence in context: A054046 A008861 A145115 this_sequence A123464 A113019 A069877
Adjacent sequences: A104141 A104142 A104143 this_sequence A104145 A104146 A104147
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KEYWORD
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nonn
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AUTHOR
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Jean Lefort (jlefort.apmep(AT)wanadoo.fr), Mar 07 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 15 2006 and again Nov 11 2006
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