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A249544
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Array read by antidiagonals: T(m,n) read in binary is a palindrome with m runs of n ones separated by single zeros.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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T(m,n) = ( 2^(n+1)^m -1 ) * ( 2^n -1 ) / ( 2^(n+1) -1 ).
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EXAMPLE
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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
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PROG
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(PHP)
// 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);
}
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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