This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A066178 Number of binary bit strings of length n with no block of 8 or more 0's. Nonzero heptanacci numbers, A122189. 26
 1, 1, 2, 4, 8, 16, 32, 64, 127, 253, 504, 1004, 2000, 3984, 7936, 15808, 31489, 62725, 124946, 248888, 495776, 987568, 1967200, 3918592, 7805695, 15548665, 30972384, 61695880, 122895984, 244804400, 487641600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Analogous bit string description and o.g.f. (1-x)/(1-2x+x^{k+1}) works for nonzero k-nacci numbers. Compositions of n into (nonzero) parts <= 7. - Joerg Arndt, Aug 06 2012 LINKS T. D. Noe, Table of n, a(n) for n = 0..200 Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. Zhao Hui Du, Link giving derivation and proof of the formula 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 Eric Weisstein's World of Mathematics, Fibonacci n-Step Number Eric Weisstein's World of Mathematics, Heptanacci Number Index entries for linear recurrences with constant coefficients, signature (1, 1, 1, 1, 1, 1, 1). FORMULA O.g.f.: 1/(1-x-x^2-x^3-x^4-x^5-x^6-x^7). a(n) = Sum_{i=n-7..n-1} a(i). a(n) = round({r-1}/{(t+1)r-2t} * r^{n-1}), where r is the heptanacci constant, the real root of the equation x^{t+1)-2x^t+1=0 which is greater than 1. The formula could also be used for a k-step Fibonacci sequence if r is replaced by the k-bonacci constant, as in A000045, A000073, A000078, A001591, A001592. - Zhao Hui Du, Aug 24 2008 For a(0)=a(1)=1, a(2)=2, a(3)=4, a(4)=8, a(5)=16, a(6)=32, a(7)=64, a(n) = 2*a(n-1) - a(n-8). - Vincenzo Librandi, Dec 20 2010 MATHEMATICA a[0] = a[1] = 1; a[2] = 2; a[3] = 4; a[4] = 8; a[5] = 16; a[6] = 32; a[7] = 64; a[n_] := 2*a[n - 1] - a[n - 8]; Array[a, 31, 0] CoefficientList[ Series[(1 - x)/(1 - 2 x + x^8), {x, 0, 30}], x] LinearRecurrence[{1, 1, 1, 1, 1, 1, 1}, {1, 1, 2, 4, 8, 16, 32}, 40] (* Harvey P. Dale, Nov 16 2014 *) CROSSREFS Cf. A000045 (k=2, Fibonacci numbers), A000073 (k=3, tribonacci) A000078 (k=4, tetranacci) A001591 (k=5, pentanacci) A001592 (k=6, hexanacci), A122189 (k=7, heptanacci). Row 7 of arrays A048887 and A092921 (k-generalized Fibonacci numbers). Sequence in context: A172316 A062258 A239560 * A122189 A194630 A251672 Adjacent sequences:  A066175 A066176 A066177 * A066179 A066180 A066181 KEYWORD nonn,easy AUTHOR Len Smiley, Dec 14 2001 EXTENSIONS Definition corrected by Vincenzo Librandi, Dec 20 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 13 01:23 EST 2019. Contains 329963 sequences. (Running on oeis4.)