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Search: id:A091913
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| A091913 |
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Matrix defined by: for n <= k, a(n,k) = 0; for n > k, a(n,k) = C(n,k) * (2^(n-k) - 1) - read by rows. |
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+0
2
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| 0, 1, 3, 2, 7, 9, 3, 15, 28, 18, 4, 31, 75, 70, 30, 5, 63, 186, 225, 140, 45, 6, 127, 441, 651, 525, 245, 63, 7, 255, 1016, 1764, 1736, 1050, 392, 84, 8, 511, 2295, 4572, 5292, 3906, 1890, 588, 108, 9, 1023, 5110, 11475, 15240, 13230, 7812, 3150, 840, 135, 10, 2047
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Rows: Sum of the n-th row = A001047(n); Sum of the n-th row excluding column 0 = A028243(n+1). Columns: a(n,0) = A000225(n); a(n,1) = A058877(n). Diagonals: a(n,n-2) = A045943(n-1). Also note that the sums of the antidiagonals = A006684.
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FORMULA
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For n <= k, a(n, k) = 0; for n > k, a(n, k) = C(n, k) * (2^(n-k) - 1). For n > k, a(n, k) = Sum [C(n,k) * C(n-k, m), {m=1 to n-k}]. [Formula corrected Aug 22 2006]
The triangle (1; 3,2; 7,9,3;...) = A007318^2 - A007318, then delete the right border of zeros. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 16 2007
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EXAMPLE
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{0}; {1}; {3,2}; {7,9,3}; {15,28,18,4}; {31,75,70,30,5}; {63,186,225,140,45,6}
a(5,3) = 30 because C(5,3) = 10, 2^(5-3) - 1 = 3 and 10 * 3 = 30.
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CROSSREFS
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Cf. A007318, A038207.
Cf. A007318.
Sequence in context: A021309 A054170 A106167 this_sequence A026136 A026172 A026186
Adjacent sequences: A091910 A091911 A091912 this_sequence A091914 A091915 A091916
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Mar 10 2004
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
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