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A060455 7th order Fibonacci numbers with a(0)=...=a(6)=1. 37
1, 1, 1, 1, 1, 1, 1, 7, 13, 25, 49, 97, 193, 385, 769, 1531, 3049, 6073, 12097, 24097, 48001, 95617, 190465, 379399, 755749, 1505425, 2998753, 5973409, 11898817, 23702017, 47213569, 94047739, 187339729, 373174033, 743349313, 1480725217 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

a(n) = number of runs in polyphase sort using 8 tapes and n-6 phases.

REFERENCES

N. Wirth, Algorithmen und Datenstrukturen, 1975, (table 2.15 chapter 2.3.4)

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..3339 (terms 0..200 from T. D. Noe)

R. L. Gilstad, Polyphase Merge Sort - Advanced Technique, Proc. AFIPS Eastern Jt. Comp. Conf. 18 (1960) 143-148.

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

FORMULA

a(n) = a(n-1)+a(n-2)+...+a(n-7) for n > 6, a(0)=a(1)=...=a(6)=1

G.f.: ( -1+x^2+2*x^3+3*x^4+4*x^5+5*x^6 ) / ( -1+x+x^2+x^3+x^4+x^5+x^6+x^7 ). - R. J. Mathar, Oct 11 2011

EXAMPLE

General formula for k-th order numbers: f(n,k)=f(n-1,k)+...+f(n-1-k,k) for n > k, else f(n,k) = 1

MAPLE

A060455 := proc(n) option remember: if n >=0 and n<=6 then RETURN(1) fi: a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7) end;

MATHEMATICA

LinearRecurrence[{1, 1, 1, 1, 1, 1, 1}, {1, 1, 1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Mar 17 2012 *)

PROG

(PARI) Vec((1-x^2-2*x^3-3*x^4-4*x^5-5*x^6)/(1-x-x^2-x^3-x^4-x^5-x^6-x^7 )+O(x^99)) \\ Charles R Greathouse IV, Feb 03 2014

CROSSREFS

For k=1..5 see A000045, A000213, A000288, A000322, A000383.

Cf. A253333, A253318: primes and indices of primes in this sequence.

Cf. A122189 Heptanacci numbers with a(0),...,a(6) = 0,0,0,0,0,0,1.

Sequence in context: A294943 A111721 A213663 * A205541 A072579 A067870

Adjacent sequences:  A060452 A060453 A060454 * A060456 A060457 A060458

KEYWORD

easy,nonn

AUTHOR

Frank Ellermann, Apr 08 2001

EXTENSIONS

More terms from James A. Sellers, Apr 11 2001

STATUS

approved

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Last modified October 23 18:46 EDT 2018. Contains 316530 sequences. (Running on oeis4.)