A272647 a(n) = A001517(n) mod 7.

1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1

Offset: 0

Author

N. J. A. Sloane, May 09 2016

Keywords

• nonn
• easy

Comments

Periodic with period length 7.

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 (0,0,0,0,0,0,1).

Crossrefs

Cf. A001517, A002119, A272648.

Cf. A010876.

Programs

Maple

f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 3 else f(n-2)+(4*n-2)*f(n-1); fi; end;
[seq(f(n) mod 7, n=0..120)];

Mathematica

PadRight[{},120,{1,3,5,4,5,3,1}] (* Harvey P. Dale, Jul 17 2020 *)

PARI

Vec((1+3*x+5*x^2+4*x^3+5*x^4+3*x^5+x^6)/((1-x)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ Colin Barker, May 10 2016

Formula

G.f.: (1 + 3*x + 5*x^2 + 4*x^3 + 5*x^4 + 3*x^5 + x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, May 10 2016

a(n) = (3*m^6 - 54*m^5 + 365*m^4 - 1140*m^3 + 1582*m^2 - 636*m + 60)/60, where m = n mod 7. - Luce ETIENNE, Oct 18 2018