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 A060455 7th order Fibonacci numbers with a(0)=...=a(6)=1. 23

%I

%S 1,1,1,1,1,1,1,7,13,25,49,97,193,385,769,1531,3049,6073,12097,24097,

%T 48001,95617,190465,379399,755749,1505425,2998753,5973409,11898817,

%U 23702017,47213569,94047739,187339729,373174033,743349313,1480725217

%N 7th order Fibonacci numbers with a(0)=...=a(6)=1.

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

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

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

%H T. D. Noe, <a href="/A060455/b060455.txt">Table of n, a(n) for n=0..200</a>

%H <a href="/index/Rea#recLCC">Index to sequences with linear recurrences with constant coefficients</a>, signature (1,1,1,1,1,1,1).

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

%F 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

%e 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

%p 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;

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

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

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

%K easy,nonn

%O 0,8

%A _Frank Ellermann_, Apr 08 2001

%E More terms from _James A. Sellers_, Apr 11 2001

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