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 A343836 #13 Aug 09 2022 11:01:22
%S A343836 0,1,1,2,-1,2,3,3,3,3,4,4,-2,4,4,5,2,-4,-4,2,5,6,6,-3,-3,-3,6,6,7,7,
%T A343836 10,-2,-2,10,7,7,8,5,8,8,-4,8,8,5,8,9,9,9,9,9,9,9,9,9,9,10,10,13,10,
%U A343836 10,-5,10,10,13,10,10,11,8,11,11,8,-7,-7,8,11,11,8,11
%N A343836 Array T(n, k), n, k > 0, read by antidiagonals; the balanced ternary representation of T(n, k) is obtained by adding componentwise (i.e., without carries) the digits in the balanced ternary representations of n and of k.
%C A343836 This sequence is similar to A003987 and to A004489.
%C A343836 We use the following table to combine individual digits (this is the balanced ternary addition table read mod 3):
%C A343836 | T 0 1
%C A343836 ---+-------
%C A343836 T | 1 T 0
%C A343836 0 | T 0 1
%C A343836 1 | 0 1 T
%H A343836 Rémy Sigrist, <a href="/A343836/b343836.txt">Table of n, a(n) for n = 0..10010</a>
%H A343836 Rémy Sigrist, <a href="/A343836/a343836.png">Colored representation of the table for n, k < 1094</a> (blue denotes negative values, red denotes positive values, dark colors correspond to small values in absolute value)
%H A343836 Wikipedia, <a href="https://en.wikipedia.org/wiki/Balanced_ternary#Addition,_subtraction_and_multiplication_and_division">Balanced ternary: Addition, subtraction and multiplication and division</a>
%F A343836 T(n, k) = T(k, n).
%F A343836 T(m, T(n, k)) = T(T(m, n), k).
%F A343836 T(n, 0) = n.
%F A343836 T(n, n) = -n.
%e A343836 Array T(n, k) begins:
%e A343836 n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A343836 ---+-----------------------------------------------------------------
%e A343836 0| 0 1 2 3 4 5 6 7 8 9 10 11 12 13
%e A343836 1| 1 -1 3 4 2 6 7 5 9 10 8 12 13 11
%e A343836 2| 2 3 -2 -4 -3 10 8 9 13 11 12 7 5 6
%e A343836 3| 3 4 -4 -3 -2 8 9 10 11 12 13 5 6 7
%e A343836 4| 4 2 -3 -2 -4 9 10 8 12 13 11 6 7 5
%e A343836 5| 5 6 10 8 9 -5 -7 -6 -11 -13 -12 -8 -10 -9
%e A343836 6| 6 7 8 9 10 -7 -6 -5 -13 -12 -11 -10 -9 -8
%e A343836 7| 7 5 9 10 8 -6 -5 -7 -12 -11 -13 -9 -8 -10
%e A343836 8| 8 9 13 11 12 -11 -13 -12 -8 -10 -9 -5 -7 -6
%e A343836 9| 9 10 11 12 13 -13 -12 -11 -10 -9 -8 -7 -6 -5
%e A343836 10| 10 8 12 13 11 -12 -11 -13 -9 -8 -10 -6 -5 -7
%e A343836 11| 11 12 7 5 6 -8 -10 -9 -5 -7 -6 -11 -13 -12
%e A343836 12| 12 13 5 6 7 -10 -9 -8 -7 -6 -5 -13 -12 -11
%e A343836 13| 13 11 6 7 5 -9 -8 -10 -6 -5 -7 -12 -11 -13
%e A343836 Array T(n, k) begins in balanced ternary:
%e A343836 n\k| 0 1 1T 10 11 1TT 1T0 1T1 10T 100 101 11T 110 111
%e A343836 ---+----------------------------------------------------------------------
%e A343836 0| 0 1 1T 10 11 1TT 1T0 1T1 10T 100 101 11T 110 111
%e A343836 1| 1 T 10 11 1T 1T0 1T1 1TT 100 101 10T 110 111 11T
%e A343836 1T| 1T 10 T1 TT T0 101 10T 100 111 11T 110 1T1 1TT 1T0
%e A343836 10| 10 11 TT T0 T1 10T 100 101 11T 110 111 1TT 1T0 1T1
%e A343836 11| 11 1T T0 T1 TT 100 101 10T 110 111 11T 1T0 1T1 1TT
%e A343836 1TT| 1TT 1T0 101 10T 100 T11 T1T T10 TT1 TTT TT0 T01 T0T T00
%e A343836 1T0| 1T0 1T1 10T 100 101 T1T T10 T11 TTT TT0 TT1 T0T T00 T01
%e A343836 1T1| 1T1 1TT 100 101 10T T10 T11 T1T TT0 TT1 TTT T00 T01 T0T
%e A343836 10T| 10T 100 111 11T 110 TT1 TTT TT0 T01 T0T T00 T11 T1T T10
%e A343836 100| 100 101 11T 110 111 TTT TT0 TT1 T0T T00 T01 T1T T10 T11
%e A343836 101| 101 10T 110 111 11T TT0 TT1 TTT T00 T01 T0T T10 T11 T1T
%e A343836 11T| 11T 110 1T1 1TT 1T0 T01 T0T T00 T11 T1T T10 TT1 TTT TT0
%e A343836 110| 110 111 1TT 1T0 1T1 T0T T00 T01 T1T T10 T11 TTT TT0 TT1
%e A343836 111| 111 11T 1T0 1T1 1TT T00 T01 T0T T10 T11 T1T TT0 TT1 TTT
%o A343836 (PARI) T(n,k,c=v->centerlift(Mod(v,3))) = { if (n==0 && k==0, return (0), my (d=c(n), t=c(k)); c(d+t)+3*T((n-d)/3, (k-t)/3)) }
%Y A343836 Cf. A003987, A004489, A343316.
%K A343836 sign,tabl,base
%O A343836 0,4
%A A343836 _Rémy Sigrist_, May 01 2021