OFFSET
1,4
COMMENTS
Row sums = A000041 starting with offset 1.
Sum of n-th row terms = leftmost term of next row, such that terms in each row demonstrate Euler's pentagonal theorem.
Let Q = triangle A027293 with partition numbers in each column.
Let M = a diagonalized variant of A080995 as the characteristic function of the generalized pentagonal numbers starting with offset 1: (1, 1, 0, 0, 1,...)
Sign the 1's: (++--++...) getting (1, 1, 0, 0, -1, 0, -1,...) which is the diagonal of matrix M, (as an infinite lower triangular matrix with the rest zeros).
Triangle A175003 = Q*M, with deleted zeros.
Column k starts at row A001318(k). - Omar E. Pol, Sep 21 2011
From Omar E. Pol, Apr 22 2014: (Start)
Row n has length A235963(n).
For Euler's pentagonal theorem for the sum of divisors see A238442.
FORMULA
EXAMPLE
Triangle begins:
1;
1, 1;
2, 1;
3, 2;
5, 3, -1;
7, 5, -1;
11, 7, -2, -1;
15, 11, -3, -1;
22, 15, -5, -2;
30, 22, -7, -3;
42, 30, -11, -5;
56, 42, -15, -7, 1;
77, 56, -22, -11, 1;
101, 77, -30, -15, 2;
...
CROSSREFS
KEYWORD
tabf,sign
AUTHOR
Gary W. Adamson, Apr 03 2010
EXTENSIONS
Corrected and extended by Omar E. Pol, Feb 14 2013
STATUS
approved