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 A147808 #14 Dec 07 2021 11:27:02
%S A147808 45,495,49500,3314850,331431000,27336542310,2733612983100,
%T A147808 238305122029260,23830484311542600,2140037814262627400,
%U A147808 214003761418373774000,19587943639318412097360,1958794348735327250973600,181693537570273520779480800
%N A147808 Sum of n-digit numbers which are balanced: the first [n/2] digits have the same sum as the last [n/2] digits.
%C A147808 Numbers such that the first half of digits have the same sum than the last half of digits are called balanced in the linked "Problem 217". (Note that here the meaning of "balanced" is neither that of A020492, nor that of A031443.)
%C A147808 Up to n=3 digits, the only balanced numbers are the palindromes, from n=4 on, there are non-palindromic balanced numbers, cf. A145808.
%H A147808 Project Euler, <a href="https://projecteuler.net/problem=217">Balanced numbers. Problem 217</a>.
%F A147808 lim a(2n+1)/a(2n) = 100, lim a(2n)/a(2n-1) = 90 (as n -> oo).
%e A147808 a(1) = 1+2+...+9; a(2) = 11+22+...+99 = 11 a(1); a(3) = 101+111+121+....+191+202+...+989+999 = (101*10 + 10*9)*a(1); a(4) = 1001+1010+1102+1111+1120+1203+...+9889+9898+9999.
%t A147808 balQ[n_]:=Module[{idn=IntegerDigits[n],len=Floor[IntegerLength[n]/2]}, Total[ Take[ idn,len]] == Total[Take[idn,-len]]]; Table[Total[ Select[ Range[ 10^n, 10^(n+1)-1],balQ]],{n,0,5}] (* This will generate the first six terms of the sequence. To generate more, (1) change the range of the Table from (0,5) to (0,6) or (0,7), etc., but the program will take increasingly long to run. *) (* _Harvey P. Dale_, Apr 07 2013 *)
%o A147808 (PARI) A147808(n)={ local( t,c ); if( n==1, 45, /* global variable SC[sd] (used for n=2k and n=2k+1) stores [sum,count] of numbers with <= n\2 digits and digit sum = sd */ if( #SC != n\2*9, SC=vector( n\2*9, digsum, c=0; [sum( i=0,10^(n\2)-1, if((i-digsum)%9==0 && digsum==sum(j=1,#t=Vecsmall(Str(i)),t[j])-48*#t, c++; i )), c] )); if( n%2==0, sum( i=10^((n\=2)-1),10^n-1, SC[A007953(i)]*[1,i*10^n]~ ), t=10^(n\=2)*[100,45]~; sum( i=10^(n-1),10^n-1, SC[A007953(i)]*[10,[i,1]*t]~ )))}
%K A147808 base,nonn
%O A147808 1,1
%A A147808 _M. F. Hasler_, Nov 23 2008
%E A147808 a(13)-a(14) from _Kevin P. Thompson_, Dec 05 2021