A358985 a(n) is the number of numbers of the form k + reverse(k) for at least one n-digit number k.

10, 18, 180, 342, 3420, 6498, 64980, 123462, 1234620, 2345778, 23457780, 44569782, 445697820, 846825858, 8468258580, 16089691302, 160896913020, 305704134738, 3057041347380, 5808378560022, 58083785600220, 110359192640418, 1103591926404180, 2096824660167942

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,19).

Formula

a(2n+1) = 10*a(2n) for n > 0. - Chai Wah Wu, Dec 09 2022

a(2n) = 19*a(2n-2) for n > 1. - Robert G. Wilson v, Dec 10 2022

a(n) = 19*a(n-2). - Wesley Ivan Hurt, Mar 17 2023

Example

There are 10 numbers of the form k + reverse(k) for 1-digit numbers k: 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18, so a(1) = 10.
There are 18 numbers of the form k + reverse(k) for 2-digit numbers k: 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, and 198, so a(2) = 18.

Mathematica

LinearRecurrence[{0, 19}, {10, 18, 180}, 30] (* Paolo Xausa, Oct 04 2024 *)

Prog

(Python)
def A358985(n):
    if n == 1:
        return 10
    kset = set()
    for i in range(10**(n-2), 10**(n-1)):
        for j in range(int((s:=str(i))[0])+1):
            kset.add(10*i+j+int(str(j)+s[::-1]))
    return len(kset) # Chai Wah Wu, Dec 09 2022
(PARI) a(n) = (18+(n<2))*19^(n\2-1)*10^(n%2); \\ Jinyuan Wang, Dec 14 2022

Crossrefs

Cf. A067030, A358986.

Sequence in context: A288781 A233451 A177172 * A171767 A153689 A240022

Adjacent sequences: A358982 A358983 A358984 * A358986 A358987 A358988

Keyword

nonn,base

Author

Jon E. Schoenfield, Dec 08 2022

Extensions

More terms from Jinyuan Wang, Dec 14 2022

Status

approved