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

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

Offset: 0

Author

Frank Ellermann, Apr 08 2001

Keywords

• easy
• nonn

Comments

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

Examples

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

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).

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.

Programs

Magma

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(  (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) )); // G. C. Greubel, Feb 03 2019

Maple

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

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^40)) \\ Charles R Greathouse IV, Feb 03 2014

Sage

((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) ).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 03 2019

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

Extensions

More terms from James Sellers, Apr 11 2001