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 A279085 #5 Jan 15 2017 11:48:49
%S A279085 1,6,44,424,4176,41696,416704,4166784,41666816
%N A279085 Number of distinct residues of triangular numbers mod 10^n.
%C A279085 Number of distinct n-digit endings of triangular numbers A000217 (written in base 10).
%F A279085 (Empirical) a(n) = (5*10^n + (9 - 2*(-1)^n)*2^n)/12.
%e A279085 The last digit of a triangular number is one of 0, 1, 3, 5, 6, or 8, so a(1) = 6. (To verify that no number from {2, 4, 7, 9} can be the last digit of a triangular number T, note that 8*T+1, which must be a square, would end with 7, 3, 7, or 3, respectively, but no square ends with 3 or 7.)
%e A279085 The 44 two-digit combinations with which a triangular number may end are 00, 01, 03, 05, 06, 10, 11, 15, 16, 20, 21, 25, 26, 28, 30, 31, 35, 36, 40, 41, 45, 46, 50, 51, 53, 55, 56, 60, 61, 65, 66, 70, 71, 75, 76, 78, 80, 81, 85, 86, 90, 91, 95, 96. Of these, there are ten combinations of each of the forms x0, x1, x5, and x6; the other four, which are the only ones that end with a digit other than 0, 1, 5, or 6, are 03, 28, 53, and 78 (i.e., numbers whose residue modulo 25 is 3):
%e A279085 .
%e A279085 last digit
%e A279085 0 1 2 3 4 5 6 7 8 9
%e A279085 +------------------------------
%e A279085 0 | 00 01 03 05 06
%e A279085 1 | 10 11 15 16
%e A279085 2 | 20 21 25 26 28
%e A279085 next-to-last 3 | 30 31 35 36
%e A279085 digit 4 | 40 41 45 46
%e A279085 5 | 50 51 53 55 56
%e A279085 6 | 60 61 65 66
%e A279085 7 | 70 71 75 76 78
%e A279085 8 | 80 81 85 86
%e A279085 9 | 90 91 95 96
%Y A279085 Cf. A000217, A000993.
%K A279085 nonn,base,more
%O A279085 0,2
%A A279085 _Jon E. Schoenfield_, Jan 14 2017