%I A145007
%S A145007 1,1,0,1,1,0,0,1,2,0,0,0,2,3,0,1,0,0,3,5,0,1,0,0,1,0,0,5,7,0,1,0,2,
%T A145007 0,0,7,11,0,0,1,0,3,0,0,11,15,0,0,0,2,0,5,0,0,15,22,0,0,0,0,3,0,7,
%U A145007 0,0,22,30,0,0,0,0,0,5,0,11,0,0,30,42,0,1,0,0,0,0,7,0,15,0,0,42,56
%V A145007 1,1,0,1,1,0,0,1,2,0,0,0,2,3,0,-1,0,0,3,5,0,-1,0,0,-1,0,0,5,7,0,-1,0,-2,
%W A145007 0,0,7,11,0,0,-1,0,-3,0,0,11,15,0,0,0,-2,0,-5,0,0,15,22,0,0,0,0,-3,0,-7,
%X A145007 0,0,22,30,0,0,0,0,0,-5,0,-11,0,0,30,42,0,1,0,0,0,0,-7,0,-15,0,0,42,56
%N A145007 Eigentriangle of the partition numbers.
%C A145007 Sum of n-th row terms = rightmost nonzero term of next row.
%C A145007 Row sums = the partition numbers, A000041, as well as the rightmost diagonal
with no zeros.
%F A145007 Triangle read by rows, termwise products of A000041 (the partition numbers);
and the partition number generator, A145006.
%e A145007 First few rows of the triangle =
%e A145007 1;
%e A145007 1, 0;
%e A145007 1, 1, 0;
%e A145007 0, 1, 2, 0;
%e A145007 0, 0, 2, 3, 0;
%e A145007 -1, 0, 0, 3, 5, 0;
%e A145007 0, -1, 0, 0, 5, 7, 0;
%e A145007 -1, 0, -2, 0, 0, 7, 11, 0,;
%e A145007 0, -1, 0, -3, 0, 0, 11, 15, 0;
%e A145007 0, 0, -2, 0, -5, 0, 0, 15, 22, 0;
%e A145007 0, 0, 0, -3, 0, -7, 0, 0, 22, 30, 0;
%e A145007 0, 0, 0, 0, -5, 0, -11, 0, 0, 30, 42, 0;
%e A145007 1, 0, 0, 0, 0, -7, 0, -15, 0, 0, 42, 56, 0;
%e A145007 0, 1, 0, 0, 0, 0, -11, 0, -22, 0, 0, 56, 77, 0;
%e A145007 0, 0, 2, 0, 0, 0, 0, -15, 0, -30, 0, 0, 77, 101, 0;
%e A145007 ...
%e A145007 Example: row 4 = (0, 0, 2, 3) = termwise products of (0, 0, 1, 1) and
(1, 1, 2, 3), where (0, 0, 1, 1) = row 4 of triangle A145006. The
partition numbers = (1, 1, 2, 3, 5, 7, 11, 15,...).
%Y A145007 Sequence in context: A057108 A063958 A126164 this_sequence A151670 A153587
A059286
%Y A145007 Adjacent sequences: A145004 A145005 A145006 this_sequence A145008 A145009
A145010
%K A145007 eigen,tabl,sign
%O A145007 0,9
%A A145007 Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 28 2008
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