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A232729 Number of n-digit numbers that yield an n-digit number after Reverse and Add. 3
4, 45, 405, 4095, 40500, 405450, 4050000, 40504500, 405000000, 4050045000, 40500000000, 405000450000, 4050000000000, 40500004500000, 405000000000000, 4050000045000000, 40500000000000000, 405000000450000000, 4050000000000000000, 40500000004500000000, 405000000000000000000 (list; graph; refs; listen; history; text; internal format)
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)

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: A123650 A122910 A117644 * A055602 A073565 A039657

Adjacent sequences:  A232726 A232727 A232728 * A232730 A232731 A232732

KEYWORD

nonn,base,easy

AUTHOR

Lars Blomberg, Nov 29 2013

STATUS

approved

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Last modified July 5 20:21 EDT 2020. Contains 335473 sequences. (Running on oeis4.)