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

1, 2, 3, 5, 4, 13, 14, 7, 14, 63, 41, 16, 17, 64, 313, 122, 43, 26, 67, 314, 1563, 365, 124, 53, 76, 317, 1564, 7813, 1094, 367, 134, 103, 326, 1567, 7814, 39063, 3281, 1096, 377, 184, 353, 1576, 7817, 39064, 195313, 9842, 3283, 1106, 427, 434, 1603, 7826, 39067, 195314

Offset: 0

Author

M. F. Hasler, Jan 01 2013

Keywords

• nonn
• tabl

Comments

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.)

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

Examples

			The upper left part of the infinite square array reads:
[   1    2    5   14   41  122  365 1094  3281 ...]
[   3    4    7   16   43  124  367 1096  3283 ...]
[  13   14   17   26   53  134  377 1106  3293 ...]
[  63   64   67   76  103  184  427 1156  3343 ...]
[ 313  314  317  326  353  434  677 1406  3593 ...]
[1563 1564 1567 1576 1603 1684 1927 2656  4843 ...]
[7813 7814 7817 7826 7853 7934 8177 8906 11093 ...]
[...]
		

Links

• Ivan Neretin, Table of n, a(n) for n = 0..5049

Programs

Mathematica

Flatten@Table[(5^j + 3^(i - j))/2, {i, 0, 8}, {j, 0, i}] (* Ivan Neretin, Sep 07 2017 *)

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

Formula

T(m,n+4) = T(m,n) (mod 10),

T(m+1,n) = T(m,n) (mod 10) for m > 0,

T(m+1,n) = T(m,n) + 50 (mod 100) for m > 1, etc. - M. F. Hasler, Jan 06 2013