A088117 Let the decimal expansion of n be abcd...; then a(n) = (a*bcd... + b*acd... + c*abd... + d*abc... + ...) + (ab*cd... + bc*ad... + cd*ab... + ...) + ... . That is, a(n) = sum over all the digit strings of the product (number obtained by deleting a digit string) * (deleted digit string).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 0, 7, 14, 21, 28, 35, 42, 49, 56, 63, 0, 8, 16, 24, 32, 40, 48, 56, 64, 72, 0, 9, 18, 27, 36, 45, 54, 63, 72, 81, 0, 11

Offset

0,13

Comments

Each substring is used in only product.

a(n) = 0 for 0 <= n <= 10.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Example

a(1234) = (1*234 + 2*134 + 3*124 + 4*123) + (12*34 + 23*14) = 2096.
a(12345) = (1*2345 + 2*1345 + 3*1245 + 4*1235 + 5*1234) + (12*345 + 15*234 + 23*145 + 34*125 + 45*123) = 40650.

Maple

a:= n-> (s-> add(add(parse(s[i..j])*parse(cat(s[1..i-1],
    s[j+1..length(s)])), i=1..j), j=1..length(s)-1))(""||n):
seq(a(n), n=0..120);  # Alois P. Heinz, May 22 2021

Crossrefs

Cf. A007954, A088116.

Different from A035930, A171765, A257850.

Sequence in context: A257297 A035930 A347470 * A349278 A195833 A257294

Adjacent sequences: A088114 A088115 A088116 * A088118 A088119 A088120

Keyword

base,easy,nonn

Author

Amarnath Murthy, Sep 25 2003

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jul 14 2007

a(0)=0 inserted and examples corrected by Alois P. Heinz, May 22 2021

Status

approved