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

0,2

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

Links

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

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

Example

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 ...]
[...]

Mathematica

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

Prog

(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

Crossrefs

Sequence in context: A061446 A280690 A240000 * A107476 A094140 A119745

Adjacent sequences: A193767 A193768 A193769 * A193771 A193772 A193773

Keyword

nonn,tabl

Author

M. F. Hasler, Jan 01 2013

Status

approved