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A079262 Octanacci numbers: a(0)=a(1)=...=a(6)=0, a(7)=1; for n >= 8, a(n) = Sum_{i=1..8} a(n-i). 9
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, 2043730736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

REFERENCES

F. T. Howard and Curtis Cooper, Some identities for r-Fibonacci numbers, http://www.math-cs.ucmo.edu/~curtisc/articles/howardcooper/genfib4.pdf.

LINKS

T. D. Noe, Table of n, a(n) for n=0..207

Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4

FORMULA

G.f.=x^7/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8). - Emeric Deutsch, 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]

Another form of tjhe g.f.: f(z)=(z^7-z^8)/(1-2*z+z^9), then a(n)=sum((-1)^i*binomial(n-7-8*i,i)*2^(n-7-9*i),i=0..floor((n-7)/9))-sum((-1)^i*binomial(n-8-8*i,i)*2^(n-8-9*i),i=0..floor((n-8)/9)) with sum(alpha(i),i=m..n))=0 for m>n. [From Richard Choulet, Feb 22 2010]

sum_{k=0..7*n} A079262(k+b)*A171890(n,k) = A079262(8*n+b), b>=0.

For a(0)=a(1)=..=a(6)=0, a(7)=a(8)=1, a(n)=2*a(n-1)-a(n-9).[From Vincenzo Librandi, Dec 20 2010]

EXAMPLE

a(16) = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255.

MAPLE

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)

for n from 0 to 50 do k(n):=sum((-1)^i*binomial(n-7-8*i, i)*2^(n-7-9*i), i=0..floor((n-7)/9))-sum((-1)^i*binomial(n-8-8*i, i)*2^(n-8-9*i), i=0..floor((n-8)/9)):od:seq(k(n), n=0..50); a:=taylor((z^7-z^8)/(1-2*z+z^9), z=0, 51); for p from 0 to 50 do j(p):=coeff(a, z, p):od :seq(j(p), p=0..50); [From Richard Choulet, Feb 22 2010]

MATHEMATICA

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 Joseph Stephan Orlovsky, Sep 30 2008]

LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 1}, 50]] (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *)

With[{nn=8}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *)

CROSSREFS

Cf. A066178, A001592, A001591, A001630, A000073, A000045.

Row 8 of arrays A048887 and A092921 (k-generalized Fibonacci numbers).

Sequence in context: A145114 A172317 A234589 * A194631 A243086 A087079

Adjacent sequences:  A079259 A079260 A079261 * A079263 A079264 A079265

KEYWORD

easy,nonn

AUTHOR

Michael Joseph Halm, Feb 04 2003

EXTENSIONS

Corrected by Joao B. Oliveira (oliveira(AT)inf.pucrs.br), Nov 25 2004

More terms from Emeric Deutsch, Apr 16 2005

STATUS

approved

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Last modified October 25 22:07 EDT 2014. Contains 248558 sequences.