A272648 a(n) = A002119(n) mod 7.
1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- D. H. Lehmer, Arithmetical periodicities of Bessel functions, Annals of Mathematics, 33 (1932): 143-150. The sequence is on page 149.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).
Programs
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GAP
b:=[1,-1];; for n in [3..95] do b[n]:=-2*(2*n-3)*b[n-1]+b[n-2]; od; a:=List(b,AbsInt) mod 7; # Muniru A Asiru, Sep 20 2018
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Maple
f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 1 else f(n-2)+(4*n-2)*f(n-1); fi; end; [seq(f(n) mod 7, n=0..120)];
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Mathematica
PadRight[{},120,{1,1,0,1,0,1,1,6,6,0,6,0,6,6}] (* Harvey P. Dale, Jun 07 2016 *) -
PARI
Vec((1+x+x^3+x^5+x^6)*(1+6*x^7)/((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ Colin Barker, May 10 2016
Formula
G.f.: (1+x+x^3+x^5+x^6)*(1+6*x^7) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, May 10 2016
a(n) = (-m^6+18*m^5-122*m^4+384*m^3-549*m^2+270*m+24)*(7-5*(-1)^floor(n/7))/48, where m = (n mod 7). - Luce ETIENNE, Sep 21 2018
Comments