A232729 Number of n-digit numbers that yield an n-digit number after Reverse and Add.

4, 45, 405, 4095, 40500, 405450, 4050000, 40504500, 405000000, 4050045000, 40500000000, 405000450000, 4050000000000, 40500004500000, 405000000000000, 4050000045000000, 40500000000000000, 405000000450000000, 4050000000000000000, 40500000004500000000, 405000000000000000000

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..990

Index entries for linear recurrences with constant coefficients, signature (10,10,-100).

Formula

a(n) + A232730(n) = 9*10^(n-1).

a(1) = 4, a(3) = 405, a(2k+1) = 100*a(2k-1), k > 1.

a(2) = 45, a(4) = 4095, a(2k) = 110*a(2k-2) - 1000*a(2k-4), k > 2.

From Colin Barker, Apr 21 2016: (Start)

a(n) = 10*a(n-1)+10*a(n-2)-100*a(n-3) for n>4.

G.f.: x*(4+5*x-85*x^2-5*x^3) / ((1-10*x)*(1-10*x^2)). (End)

E.g.f.: (81*cosh(10*x) + 90*cosh(sqrt(10)*x) + 81*sinh(10*x) - 10*x - 171)/200. - Stefano Spezia, Oct 27 2022

Example

There are 4 1-digit numbers (1,2,3,4) that yield a 1-digit number (2,4,6,8), so a(1)=4.

Prog

(PARI) Vec(x*(4+5*x-85*x^2-5*x^3)/((1-10*x)*(1-10*x^2)) + O(x^50)) \\ Colin Barker, Apr 22 2016

Crossrefs

Cf. A232730, A232731.

Sequence in context: A122910 A343904 A117644 * A055602 A346629 A073565

Adjacent sequences: A232726 A232727 A232728 * A232730 A232731 A232732

Keyword

nonn,base,easy

Author

Lars Blomberg, Nov 29 2013

Status

approved