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A193770
Table T(m,n) = (5^m + 3^n)/2, m,n = 0,1,2,..., read by antidiagonals.
3
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
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
KEYWORD
nonn,tabl
AUTHOR
M. F. Hasler, Jan 01 2013
STATUS
approved