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A232730 Number of n-digit numbers that yield an (n+1)-digit number after Reverse and Add. 3
5, 45, 495, 4905, 49500, 494550, 4950000, 49495500, 495000000, 4949955000, 49500000000, 494999550000, 4950000000000, 49499995500000, 495000000000000, 4949999955000000, 49500000000000000, 494999999550000000, 4950000000000000000, 49499999995500000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A232729(n) + a(n) = 9*10^(n-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(1) = 5, a(3) = 495, a(2*k+1) = 100*a(2*k-1), k > 1.

a(2) = 45, a(4) = 4905, a(2*k) = 110*a(2*k-2) - 1000*a(2*k-4), k > 2.

G.f. = 5*x*(1+x)*(1-x)^2 / ((1-10*x)*(1-10*x^2)). - M. F. Hasler, Nov 30 2013

From Colin Barker, Mar 20 2017: (Start)

a(n) = -45*(10^(n/2-2) - 11*10^(n-3)) for n>2 even.

a(n) = 99*2^(n-3)*5^(n-2) for n>2 odd.

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

(End)

EXAMPLE

There are 5 1-digit numbers (5,6,7,8,9) that yield a 2-digit number (10,12,14,16,18), so a(1)=5.

MAPLE

a[1]:=5: t[0]:= 0: t[1]:= 5:

for n from 2 to 50 do

a[n]:= 45*10^(n-2) + 9*t[n-2];

t[n]:= a[n] + t[n-2];

od:

seq(a[n], n=1..50); # Robert Israel, Apr 21 2016

PROG

(PARI) Vec(5*x*(1+x)*(1-x)^2 / ((1-10*x)*(1-10*x^2)) + O(x^30)) \\ Colin Barker, Mar 20 2017

CROSSREFS

Cf. A232729, A232731.

Sequence in context: A191095 A202825 A195188 * A151831 A233834 A188267

Adjacent sequences:  A232727 A232728 A232729 * A232731 A232732 A232733

KEYWORD

nonn,base,easy

AUTHOR

Lars Blomberg, Nov 29 2013

EXTENSIONS

G.f. corrected and empirical formulas proved by Robert Israel, Apr 21 2016

STATUS

approved

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Last modified July 6 23:56 EDT 2020. Contains 335484 sequences. (Running on oeis4.)