This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138953 #23 May 13 2013 19:04:39
%S A138953 0,0,0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,11,3,4,5,
%T A138953 6,7,8,9,10,11,12,4,5,6,7,8,9,10,11,12,13,5,6,7,8,9,10,11,12,13,14,6,
%U A138953 7,8,9,10,11,12,13,14,15,7,8,9,10,11,12,13,14,15,16,8,9,10,11,12,13,14,15
%N A138953 Sum of numbers from all substrings of n.
%H A138953 Zak Seidov and Christian N. K. Anderson, <a href="/A138953/b138953.txt">Table of n, a(n) for n = 0..10000</a> (first 1000 terms from Zak Seidov)
%F A138953 a(n) = A071980(n) - n. [_R. J. Mathar_, Jul 06 2009]
%F A138953 Note: Mathar's formula works for numbers with 1, 2 or 3 digits, but thereafter only for numbers whose internal digits are zeros. [_Christian N. K. Anderson_, May 13 2013]
%e A138953 One-digit numbers have no substring, hence a(0..9)=0;
%e A138953 a(10) = 1+0 = 1,
%e A138953 a(123) = 1+2+3+12+23 = 41,
%e A138953 a(150) = 1+5+0+15+50 = 71.
%t A138953 Table[id=IntegerDigits[n]; Total[Flatten[Table[FromDigits/@ Partition[id,k,1], {k,Length[id]-1}]]], {n,0,150}]
%Y A138953 Cf. A093882.
%K A138953 nonn,base
%O A138953 0,12
%A A138953 _Zak Seidov_, Apr 04 2008