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Search: id:A153279
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| A153279 |
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Eigentriangle by rows, T(n,k) = A000079(n-k) * (diagonalized matrix of (1,1,3,9,27,81,...)). |
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3
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| 1, 2, 1, 4, 2, 3, 8, 4, 6, 9, 16, 8, 12, 18, 27, 32, 16, 24, 36, 54, 81, 64, 32, 48, 72, 108, 162, 243, 128, 64, 96, 144, 216, 324, 486, 729, 256, 128, 192, 288, 432, 648, 972, 1458, 2187, 512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row sums = 3^n
Sum of n-th row terms = rightmost term of next row.
Eigensequence of the triangle = A153280: (1, 3, 15, 165, 4785, 397155,...)
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FORMULA
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Triangle read by rows, M*Q. M = triangle T(n,k) = A000079(n-k); powers of 2 in every column. Q = an infinite lower triangular matrix with powers of 3 prefaced with a 1: (1,1,3,9,27,...) as the main diagonal and the rest zeros.
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EXAMPLE
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First few rows of the triangle =
1;
2, 1;
4, 2, 3;
8, 4, 6, 9;
16, 8, 12, 18, 27;
32, 16, 24, 36, 54, 81;
64, 32, 48, 72, 108, 162, 243;
128, 64, 96, 144, 216, 324, 486, 729;
256, 128, 192, 288, 432, 648, 972, 1458, 2187;
512, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561;
...
Row 3 = (8, 4, 6, 9) = termwise products of (8, 4, 2, 1) and (1, 1, 3, 9).
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CROSSREFS
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Cf. A000079, A000244, A153280
Sequence in context: A036998 A121464 A090278 this_sequence A082908 A086449 A070556
Adjacent sequences: A153276 A153277 A153278 this_sequence A153280 A153281 A153282
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 23 2008
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