A249544 Array read by antidiagonals: T(m,n) read in binary is a palindrome with m runs of n ones separated by single zeros.

1, 3, 5, 7, 27, 21, 15, 119, 219, 85, 31, 495, 1911, 1755, 341, 63, 2015, 15855, 30583, 14043, 1365, 127, 8127, 128991, 507375, 489335, 112347, 5461, 255, 32639, 1040319, 8255455, 16236015, 7829367, 898779, 21845, 511, 130815, 8355711

Offset: 1

Author

Tilman Piesk, Oct 31 2014

Keywords

• nonn
• tabl

Comments

The entries in this array are all in A194602, and therefore can be interpreted as integer partitions: T(m,n) is the integer partition with m times the addend n+1, and no other non-one addends. The array A249543 contains the corresponding indices of A194602.

Examples

			Array starts:                                          Binary:
  n    1      2       3         4          5
m
1      1      3       7        15         31               1        11          111
2      5     27     119       495       2015             101     11011      1110111
3     21    219    1911     15855     128991           10101  11011011  11101110111
4     85   1755   30583    507375    8255455
5    341  14043  489335  16236015  528349151
		

Links

• Tilman Piesk, First 113 rows of the triangle, flattened

Crossrefs

Cf. A249543, A194602; Rows: A000225, A129868; Columns: A002450, A083713.

Programs

PHP

A249544($m, $n) {
// a                  b            c
// ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 )
$a = gmp_sub( gmp_pow( gmp_pow(2,$n+1), $m ), 1 );
$b = gmp_sub( gmp_pow(2,$n), 1 );
$c = gmp_sub( gmp_pow(2,$n+1), 1 );
$return = gmp_div_q( gmp_mul($a,$b), $c );
return gmp_strval($return);
}

Formula

T(m,n) = ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 ).