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

%I A249544 #30 Nov 02 2021 22:24:40
%S A249544 1,3,5,7,27,21,15,119,219,85,31,495,1911,1755,341,63,2015,15855,30583,
%T A249544 14043,1365,127,8127,128991,507375,489335,112347,5461,255,32639,
%U A249544 1040319,8255455,16236015,7829367,898779,21845,511,130815,8355711
%N A249544 Array read by antidiagonals: T(m,n) read in binary is a palindrome with m runs of n ones separated by single zeros.
%C A249544 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 A249544 Tilman Piesk, <a href="/A249544/b249544.txt">First 113 rows of the triangle, flattened</a>
%F A249544 T(m,n) = ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 ).
%e A249544 Array starts:                                          Binary:
%e A249544   n    1      2       3         4          5
%e A249544 m
%e A249544 1      1      3       7        15         31               1        11          111
%e A249544 2      5     27     119       495       2015             101     11011      1110111
%e A249544 3     21    219    1911     15855     128991           10101  11011011  11101110111
%e A249544 4     85   1755   30583    507375    8255455
%e A249544 5    341  14043  489335  16236015  528349151
%o A249544 (PHP)
%o A249544 <?php function A249544($m, $n) {
%o A249544 // a                  b            c
%o A249544 // ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 )
%o A249544 $a = gmp_sub( gmp_pow( gmp_pow(2,$n+1), $m ), 1 );
%o A249544 $b = gmp_sub( gmp_pow(2,$n), 1 );
%o A249544 $c = gmp_sub( gmp_pow(2,$n+1), 1 );
%o A249544 $return = gmp_div_q( gmp_mul($a,$b), $c );
%o A249544 return gmp_strval($return);
%o A249544 }
%Y A249544 Cf. A249543, A194602; Rows: A000225, A129868; Columns: A002450, A083713.
%K A249544 nonn,tabl
%O A249544 1,2
%A A249544 _Tilman Piesk_, Oct 31 2014