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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). 27
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

LINKS

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

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

F. T. Howard and Curtis Cooper, Some identities for r-Fibonacci numbers.

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

Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1).

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)..a(9) = 1, 1, 2, 4, 8, 16, 32, 64, 128. a(10) and following are given by 63*2^(n-8)+(1/2+sqrt(5/4))^(n-6)/sqrt(5)-(1/2-sqrt(5/4))^(n-6)/sqrt(5). Offset 10. a(10)=255. - Al Hakanson (hawkuu(AT)gmail.com), Feb 14 2009

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

sum_{k=0..7*n} a(k+b)*A171890(n,k) = a(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). - 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); # Emeric Deutsch, Apr 16 2005

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); # 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 (* 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).

Cf. A253706, A253705. Primes and indices of primes in this sequence.

Sequence in context: A145114 A172317 A234589 * A194631 A251746 A251760

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 July 4 02:59 EDT 2015. Contains 259187 sequences.