A212594 a(n) is the difference between multiples of 11 with even and odd decimal digit sum in interval [0,10^n).

1, 10, 19, 430, 841, 20602, 40363, 995710, 1951057, 48162410, 94373763, 2329795534, 4565217305, 112701782490, 220838347675, 5451852478622, 10682866609569, 263728727794378, 516774588979187, 12757653047779310, 24998531506579433, 617140623134480698

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 (0,55,0,-330,0,462,0,-165,0,11).

Crossrefs

Cf. A038754, A212500, A212592, A212593, A091042.

Programs

Magma

m:=23; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1+10*x-36*x^2-120*x^3+126*x^4+252*x^5-84*x^6-120*x^7+9*x^8+10*x^9)/(1-55*x^2+330*x^4-462*x^6+165*x^8-11*x^10))); // Bruno Berselli, May 22 2012

Mathematica

LinearRecurrence[{0, 55, 0, -330, 0, 462, 0, -165, 0, 11}, {1, 10, 19, 430, 841, 20602, 40363, 995710, 1951057, 48162410}, 22] (* Bruno Berselli, May 22 2012 *)

Formula

For n>=11, a(n) = 55*a(n-2)-330*a(n-4)+462*a(n-6)-165*a(n-8)+11*a(n-10).

G.f.: x*(1+10*x-36*x^2-120*x^3+126*x^4+252*x^5-84*x^6-120*x^7+9*x^8+10*x^9)/(1-55*x^2+330*x^4-462*x^6+165*x^8-11*x^10). [Bruno Berselli, May 22 2012]