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

0,2

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A001517, A002119, A272648.

Cf. A010876.

Sequence in context: A019707 A197825 A077861 * A076308 A049528 A206035

Adjacent sequences: A272644 A272645 A272646 * A272648 A272649 A272650

Keyword

nonn,easy

Author

N. J. A. Sloane, May 09 2016

Status

approved