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A132193
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Triangle whose n-th row is the list in increasing order of the integers which are the sum of squares of positive integers with sum n. The n-th row begins with n and ends with n^2.
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1
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0, 1, 2, 4, 3, 5, 9, 4, 6, 8, 10, 16, 5, 7, 9, 11, 13, 17, 25, 6, 8, 10, 12, 14, 18, 20, 26, 36, 7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 37, 49, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 38, 40, 50, 64, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 39, 41, 45, 51, 53, 65, 81
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OFFSET
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0,3
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COMMENTS
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The n-th row is the list of possible dimensions of the commutant space of an n X n matrix A, i.e. the set of matrices M such that AM=MA. The number of elements in the n-th row is given by the sequence A069999. - Corrected by Ricardo C. Santamaria, Nov 08 2012
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LINKS
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EXAMPLE
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T(4,1)=4 because 4=1+1+1+1 and 1^2+1^2+1^2+1^2=4 ; T(4,2)=6 because 4=2+1+1 and 2^2+1^2+1^2=6.
Triangle T(n,k) begins:
0;
1;
2, 4;
3, 5, 9;
4, 6, 8, 10, 16;
5, 7, 9, 11, 13, 17, 25;
6, 8, 10, 12, 14, 18, 20, 26, 36;
7, 9, 11, 13, 15, 17, 19, 21, 25, 27, 29, 37, 49;
...
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0 or i=1, {n},
{b(n, i-1)[], map(x-> x+i^2, b(n-i, min(n-i, i)))[]})
end:
T:= n-> sort([b(n$2)[]])[]:
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MATHEMATICA
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selQ[n_][p_] := MemberQ[#.# & /@ IntegerPartitions[n], p]; row[n_] := Select[Range[n, n^2], selQ[n] ]; Table[row[n], {n, 1, 10}] // Flatten (* Jean-François Alcover, Dec 11 2013 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Ricardo C. Santamaria, Nov 08 2012
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STATUS
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approved
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