A249544 - OEIS

%I #30 Nov 02 2021 22:24:40

%S 1,3,5,7,27,21,15,119,219,85,31,495,1911,1755,341,63,2015,15855,30583,

%T 14043,1365,127,8127,128991,507375,489335,112347,5461,255,32639,

%U 1040319,8255455,16236015,7829367,898779,21845,511,130815,8355711

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

%C 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.

%H Tilman Piesk, <a href="/A249544/b249544.txt">First 113 rows of the triangle, flattened</a>

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

%e Array starts:                                          Binary:

%e   n    1      2       3         4          5

%e m

%e 1      1      3       7        15         31               1        11          111

%e 2      5     27     119       495       2015             101     11011      1110111

%e 3     21    219    1911     15855     128991           10101  11011011  11101110111

%e 4     85   1755   30583    507375    8255455

%e 5    341  14043  489335  16236015  528349151

%o (PHP)

%o <?php function A249544($m, $n) {

%o // a                  b            c

%o // ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 )

%o $a = gmp_sub( gmp_pow( gmp_pow(2,$n+1), $m ), 1 );

%o $b = gmp_sub( gmp_pow(2,$n), 1 );

%o $c = gmp_sub( gmp_pow(2,$n+1), 1 );

%o $return = gmp_div_q( gmp_mul($a,$b), $c );

%o return gmp_strval($return);

%o }

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

%K nonn,tabl

%O 1,2

%A _Tilman Piesk_, Oct 31 2014