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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 09 2016
STATUS
approved