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A143866
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Eigentriangle of A027293.
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2
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1, 1, 1, 2, 1, 2, 3, 2, 2, 5, 5, 3, 4, 5, 12, 7, 5, 6, 10, 12, 29, 11, 7, 10, 15, 24, 29, 69, 15, 11, 14, 25, 36, 58, 69, 165, 22, 15, 22, 35, 60, 87, 138, 165, 393, 937, 42, 30, 44, 75, 132, 203, 345, 495, 786, 937, 2233, 56, 42, 60, 110, 180, 319, 483, 825, 1179, 1874, 2233, 5322
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OFFSET
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1,4
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COMMENTS
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Left border = partition numbers, A000041 starting (1, 1, 2, 3, 5, 7, ...). Right border = INVERT transform of partition numbers starting (1, 1, 2, 5, 12, ...); with row sums the same sequence but starting (1, 2, 5, 12, ...). Sum of n-th row terms = rightmost term of next row.
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LINKS
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FORMULA
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Triangle read by rows, A027293 * (A067687 * 0^(n-k)); 1 <= k <= n. (A067687 * 0^(n-k)) = an infinite lower triangular matrix with the INVERT transform of the partition function as the main diagonal: (1, 1, 2, 5, 12, 29, 69, 165, ...); and the rest zeros. Triangle A027293 = n terms of "partition numbers decrescendo"; by rows = termwise product of n terms of partition decrescendo and n terms of A027293: (1, 1, 2, 5, 12, 29, 69, 165, ...).
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EXAMPLE
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The triangle begins:
n \ k 1 2 3 4 5 6 7 8 9 10 11 ...
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1: 1
2: 1 1
3: 2 1 2
4: 3 2 2 5
5: 5 3 4 5 12
6: 7 5 6 10 12 29
7: 11 7 10 15 24 29 69
8: 15 11 14 25 36 58 69 165
9: 22 15 22 35 60 87 138 165 393
10: 30 22 30 55 84 145 207 330 393 937
11: 42 30 44 75 132 203 345 495 786 937 2233
Row 4 = (3, 2, 2, 5) = termwise product of (3, 2, 1, 1) and (1, 1, 2, 5) = (3*1, 2*1, 1*2, 1*5).
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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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