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A193770 Table T(m,n) = (5^m + 3^n)/2, m,n = 0,1,2,..., read by antidiagonals.

%I A193770 #19 Feb 23 2019 04:22:32
%S A193770 1,2,3,5,4,13,14,7,14,63,41,16,17,64,313,122,43,26,67,314,1563,365,
%T A193770 124,53,76,317,1564,7813,1094,367,134,103,326,1567,7814,39063,3281,
%U A193770 1096,377,184,353,1576,7817,39064,195313,9842,3283,1106,427,434,1603,7826,39067,195314
%N A193770 Table T(m,n) = (5^m + 3^n)/2, m,n = 0,1,2,..., read by antidiagonals.
%C A193770 Sequence A193769 lists the elements of the array in order of increasing size. Sequence A081458 is the subtable with every other row and column deleted (i.e., m,n=0,2,4,...). (The earlier existence of that table in the OEIS has motivated the definition of the present sequence/table.)
%C A193770 Looking at the example one can notice the periodicity of the final digit(s) of the terms; it is easy to prove these formulas. - _M. F. Hasler_, Jan 06 2013
%H A193770 Ivan Neretin, <a href="/A193770/b193770.txt">Table of n, a(n) for n = 0..5049</a>
%F A193770 T(m,n+4) = T(m,n) (mod 10),
%F A193770 T(m+1,n) = T(m,n) (mod 10) for m > 0,
%F A193770 T(m+1,n) = T(m,n) + 50 (mod 100) for m > 1, etc. - _M. F. Hasler_, Jan 06 2013
%e A193770 The upper left part of the infinite square array reads:
%e A193770 [   1    2    5   14   41  122  365 1094  3281 ...]
%e A193770 [   3    4    7   16   43  124  367 1096  3283 ...]
%e A193770 [  13   14   17   26   53  134  377 1106  3293 ...]
%e A193770 [  63   64   67   76  103  184  427 1156  3343 ...]
%e A193770 [ 313  314  317  326  353  434  677 1406  3593 ...]
%e A193770 [1563 1564 1567 1576 1603 1684 1927 2656  4843 ...]
%e A193770 [7813 7814 7817 7826 7853 7934 8177 8906 11093 ...]
%e A193770 [...]
%t A193770 Flatten@Table[(5^j + 3^(i - j))/2, {i, 0, 8}, {j, 0, i}] (* _Ivan Neretin_, Sep 07 2017 *)
%o A193770 (PARI) for(x=0,10,for(y=0,x, print1((3^(x-y)+5^y)/2 ","))) \\ prints this sequence; to get the table, use matrix(7,9,m,n,3^n/3+5^m/5)/2 \\ _M. F. Hasler_, Jan 06 2013
%K A193770 nonn,tabl
%O A193770 0,2
%A A193770 _M. F. Hasler_, Jan 01 2013