OFFSET
1,1
COMMENTS
a(n) is the difference between numbers of nonnegative multiples of 2*n+1 with even and odd digit sum in base 2*n in interval [0, 64*n^6).
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
V. Shevelev, On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m, arXiv:0710.3177 [math.NT], 2007.
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^6(Pi*i/(2*n+1)).
G.f.: 2*x*(9+116*x+126*x^2+4*x^3+x^4) / (1-x)^6. - Colin Barker, Dec 01 2015
PROG
(PARI) Vec(2*x*(9+116*x+126*x^2+4*x^3+x^4)/(1-x)^6 + O(x^50)) \\ Colin Barker, Dec 01 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, May 23 2012
STATUS
approved