A212593 a(n) is the difference between multiples of 9 with even and odd digit sum in base 8 in interval [0,8^n).

1, 8, 15, 232, 449, 7400, 14351, 237832, 461313, 7648968, 14836623, 246015528, 477194433, 7912700328, 15348206223, 254499628104, 493651049985, 8185582834056, 15877514618127, 263276481572712, 510675448527297, 8467876653984360

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, May 22 2012

Keywords

• nonn
• base
• easy

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 (0,36,0,-126,0,84,0,-9).

Crossrefs

Cf. A038754, A212500, A212592, A091042.

Programs

Mathematica

LinearRecurrence[{0, 36, 0, -126, 0, 84, 0, -9}, {1, 8, 15, 232, 449, 7400, 14351, 237832}, 22] (* Bruno Berselli, May 22 2012 *)

Formula

For n>=9, a(n) = 36*a(n-2)-126*a(n-4)+84*a(n-6)-9*a(n-8).

G.f.: x*(1+8*x-21*x^2-56*x^3+35*x^4+56*x^5-7*x^6-8*x^7)/((1-3*x^2)*(1-33*x^2+27*x^4-3*x^6)). [Bruno Berselli, May 22 2012]