cp's OEIS Frontend

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).

%I A088117 #35 May 22 2021 03:10:15
%S A088117 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,
%T A088117 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,
%U A088117 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
%N 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).
%C A088117 Each substring is used in only product.
%C A088117 a(n) = 0 for 0 <= n <= 10.
%H A088117 Alois P. Heinz, <a href="/A088117/b088117.txt">Table of n, a(n) for n = 0..20000</a>
%e A088117 a(1234) = (1*234 + 2*134 + 3*124 + 4*123) + (12*34 + 23*14) = 2096.
%e A088117 a(12345) = (1*2345 + 2*1345 + 3*1245 + 4*1235 + 5*1234) + (12*345 + 15*234 + 23*145 + 34*125 + 45*123) = 40650.
%p A088117 a:= n-> (s-> add(add(parse(s[i..j])*parse(cat(s[1..i-1],
%p A088117     s[j+1..length(s)])), i=1..j), j=1..length(s)-1))(""||n):
%p A088117 seq(a(n), n=0..120);  # _Alois P. Heinz_, May 22 2021
%Y A088117 Cf. A007954, A088116.
%Y A088117 Different from A035930, A171765, A257850.
%K A088117 base,easy,nonn
%O A088117 0,13
%A A088117 _Amarnath Murthy_, Sep 25 2003
%E A088117 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jul 14 2007
%E A088117 a(0)=0 inserted and examples corrected by _Alois P. Heinz_, May 22 2021