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A092080 Triangle read by rows in which row n lists the partition numbers of the first n positive integers.

%I A092080 #13 Apr 26 2012 11:22:01
%S A092080 1,1,2,1,2,3,1,2,3,5,1,2,3,5,7,1,2,3,5,7,11,1,2,3,5,7,11,15,1,2,3,5,7,
%T A092080 11,15,22,1,2,3,5,7,11,15,22,30,1,2,3,5,7,11,15,22,30,42,1,2,3,5,7,11,
%U A092080 15,22,30,42,56,1,2,3,5,7,11,15,22,30,42,56,77,1,2,3,5,7,11,15,22,30,42
%N A092080 Triangle read by rows in which row n lists the partition numbers of the first n positive integers.
%C A092080 Sequence of row lengths of array A092078.
%C A092080 Interpreted as a sequence a(n) = p(m) = A000041(m) (number of partitions of m) with m := n-L, where L is the largest number from A000217 (triangular numbers) which is less than n.
%C A092080 Row sums give A026905. - _Omar E. Pol_, Apr 23 2012
%F A092080 T(n,k) = A000041(k), k >= 1. - _Omar E. Pol_, Apr 23 2012
%e A092080 a(17)= p(2)= 2 because 17 = (15=A000217(5)) + 2.
%e A092080 a(10)= p(4)= 5 because 10 = (6=A000217(3)) + 4 (note that T < n, not <=n, is asked for).
%e A092080 Contribution from _Omar E. Pol_, Apr 24 2012 (Start):
%e A092080 Triangle begins:
%e A092080 1;
%e A092080 1, 2;
%e A092080 1, 2, 3;
%e A092080 1, 2, 3, 5;
%e A092080 1, 2, 3, 5, 7;
%e A092080 1, 2, 3, 5, 7, 11;
%e A092080 1, 2, 3, 5, 7, 11, 15;
%e A092080 1, 2, 3, 5, 7, 11, 15, 22;
%e A092080 1, 2, 3, 5, 7, 11, 15, 22, 30;
%e A092080 1, 2, 3, 5, 7, 11, 15, 22, 30, 42;
%e A092080 (End)
%Y A092080 Cf. A000041.
%K A092080 nonn,tabl,easy
%O A092080 1,3
%A A092080 _Wolfdieter Lang_, Mar 19 2004
%E A092080 Better definition from _Omar E. Pol_, Apr 24 2012