OFFSET
1,2
COMMENTS
In general for all z, given a sequence of the form: a(n) is the difference between multiples of 2z+1 with even and odd digit sum in base 2z in interval [0,(2z)^n); then a(n) = (a(n+1) + a(n-1))/2 when n is even. The equation applies here where z=3. - Bob Selcoe, Jun 10 2014
LINKS
Vladimir 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 (0,21,0,-35,0,7).
FORMULA
For n>=7, a(n) = 21*a(n-2)-35*a(n-4)+7*a(n-6).
G.f.: x*(1+6*x-10*x^2-20*x^3+5*x^4+6*x^5)/(1-21*x^2+35*x^4-7*x^6). [Bruno Berselli, May 22 2012]
a(n) = 2a(n-1) - a(n-2) when n is odd; a(n) = (a(n+1) + a(n-1))/2 when n is even. - Bob Selcoe, Jun 10 2014
MATHEMATICA
LinearRecurrence[{0, 21, 0, -35, 0, 7}, {1, 6, 11, 106, 201, 2022}, 24] (* Bruno Berselli, May 22 2012 *)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Vladimir Shevelev and Peter J. C. Moses, May 22 2012
STATUS
approved