A232730 -id:A232730 - cp's OEIS frontend

A232731 Number of numbers that yield an n-digit number after Reverse and Add!.

4, 50, 450, 4590, 45405, 454950, 4544550, 45454500, 454495500, 4545045000, 45449955000, 454500450000, 4544999550000, 45450004500000, 454499995500000, 4545000045000000, 45449999955000000, 454500000450000000, 4544999999550000000, 45450000004500000000

Offset: 1

Lars Blomberg, Nov 29 2013

A190481 is the number of distinct n-digit numbers after Reverse and Add!.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (10,10,-100).

Cf. A190481, A232729, A232730.

LinearRecurrence[{10,10,-100},{4,50,450,4590,45405},20] (* Harvey P. Dale, Sep 22 2017 *)

Vec(x*(4 + 10*x - 90*x^2 - 10*x^3 + 5*x^4) / ((1 - 10*x)*(1 - 10*x^2)) + O(x^30)) \\ Colin Barker, Mar 20 2017

a(1) = A232729(1), a(n) = A232729(n) + A232730(n-1), n > 1.
From Colin Barker, Mar 20 2017: (Start)
G.f.: x*(4 + 10*x - 90*x^2 - 10*x^3 + 5*x^4) / ((1 - 10*x)*(1 - 10*x^2)).
a(n) = 10*a(n-1) + 10*a(n-2) - 100*a(n-3) for n>5.
(End)

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

Original entry on oeis.org

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

Offset: 1

Lars Blomberg, Nov 29 2013

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

Robert Israel, Table of n, a(n) for n = 1..990
Index entries for linear recurrences with constant coefficients, signature (10,10,-100).

Cf. A232730, A232731.

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

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

cp's OEIS Frontend

A232731 Number of numbers that yield an n-digit number after Reverse and Add!.

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