%I #19 Feb 23 2019 04:22:32
%S 1,2,3,5,4,13,14,7,14,63,41,16,17,64,313,122,43,26,67,314,1563,365,
%T 124,53,76,317,1564,7813,1094,367,134,103,326,1567,7814,39063,3281,
%U 1096,377,184,353,1576,7817,39064,195313,9842,3283,1106,427,434,1603,7826,39067,195314
%N Table T(m,n) = (5^m + 3^n)/2, m,n = 0,1,2,..., read by antidiagonals.
%C 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 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 Ivan Neretin, <a href="/A193770/b193770.txt">Table of n, a(n) for n = 0..5049</a>
%F T(m,n+4) = T(m,n) (mod 10),
%F T(m+1,n) = T(m,n) (mod 10) for m > 0,
%F T(m+1,n) = T(m,n) + 50 (mod 100) for m > 1, etc. - _M. F. Hasler_, Jan 06 2013
%e The upper left part of the infinite square array reads:
%e [ 1 2 5 14 41 122 365 1094 3281 ...]
%e [ 3 4 7 16 43 124 367 1096 3283 ...]
%e [ 13 14 17 26 53 134 377 1106 3293 ...]
%e [ 63 64 67 76 103 184 427 1156 3343 ...]
%e [ 313 314 317 326 353 434 677 1406 3593 ...]
%e [1563 1564 1567 1576 1603 1684 1927 2656 4843 ...]
%e [7813 7814 7817 7826 7853 7934 8177 8906 11093 ...]
%e [...]
%t Flatten@Table[(5^j + 3^(i - j))/2, {i, 0, 8}, {j, 0, i}] (* _Ivan Neretin_, Sep 07 2017 *)
%o (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 nonn,tabl
%O 0,2
%A _M. F. Hasler_, Jan 01 2013