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Search: id:A079262
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| A079262 |
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Octanacci numbers: a(0)=a(1)=...=a(6)=0, a(7)=1; for n >= 8, a(n) = Sum_{i=1..8} a(n-i). |
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+0
8
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| 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 255, 509, 1016, 2028, 4048, 8080, 16128, 32192, 64256, 128257, 256005, 510994, 1019960, 2035872, 4063664, 8111200, 16190208, 32316160, 64504063, 128752121, 256993248, 512966536, 1023897200
(list; graph; listen)
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OFFSET
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0,10
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REFERENCES
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Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..207
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FORMULA
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G.f.=x^7/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2005
a(1-9)=1,1,2,4,8,16,32,64,128. a(10 & following)=63*2^(n-8)+(.5+sqrt1.25)^(n-6)/sqrt5-(.5-sqrt1.25)^(n-6)/sqrt5. Offset 10. a(10)=255. [From Al Hakanson (hawkuu(AT)gmail.com), Feb 14 2009]
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EXAMPLE
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a(16) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.
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MAPLE
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for j from 0 to 6 do a[j]:=0 od: a[7]:=1: for n from 8 to 45 do a[n]:=sum(a[n-i], i=1..8) od:seq(a[n], n=0..45); (Deutsch)
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MATHEMATICA
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a=0; b=0; c=0; d=0; e=0; f=0; g=0; h=1; lst={a, b, c, d, e, f, g, h}; Do[k=a+b+c+d+e+f+g+h; AppendTo[lst, k]; a=b; b=c; c=d; d=e; e=f; f=g; g=h; h=k, {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008]
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CROSSREFS
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Cf. A066178, A001592, A001591, A001630, A000073, A000045.
Row 8 of arrays A048887 and A092921 (k-generalized Fibonacci numbers).
Sequence in context: A054045 A008860 A145114 this_sequence A087079 A009694 A097000
Adjacent sequences: A079259 A079260 A079261 this_sequence A079263 A079264 A079265
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KEYWORD
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easy,nonn
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AUTHOR
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Michael Joseph Halm (hierogamous(AT)lycos.com), Feb 04 2003
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EXTENSIONS
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Corrected by Joao B. Oliveira (oliveira(AT)inf.pucrs.br), Nov 25 2004
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 16 2005
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