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Search: id:A112626
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| A112626 |
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Array, a(n,k) = Sum[C(n,k+m)2^(n-k-m),{m,0,n}], read by rows. |
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+0
6
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| 1, 3, 1, 9, 5, 1, 27, 19, 7, 1, 81, 65, 33, 9, 1, 243, 211, 131, 51, 11, 1, 729, 665, 473, 233, 73, 13, 1, 2187, 2059, 1611, 939, 379, 99, 15, 1, 6561, 6305, 5281, 3489, 1697, 577, 129, 17, 1, 19683, 19171, 16867, 12259, 6883, 2851, 835, 163, 19, 1, 59049, 58025
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 is the row sums of A038207 starting at column 0, column 1 is the row sums of A038207 starting at column 1 etc. etc. Helpful suggestions related to Riordan arrays given by Paul Barry.
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REFERENCES
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Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
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FORMULA
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a(n, k) = Sum[C(n, k+m)2^(n-k-m), {m, 0, n}]. O.g.f. (by columns) = x^k / (1-3x)(1-2x)^k (Frank Ruskey and class).
a(n,k) = Sum[C(n,m)2^(n-m),{m,k,n}]. - Ross La Haye (rlahaye(AT)new.rr.com), May 02 2006
Binomial transform (by columns) of A055248.
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EXAMPLE
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{1};{3,1};{9,5,1};{27,19,7,1};{81,65,33,9,1};{243,211,131,51,11,1};{729,665,473,233,73,13,1}
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MATHEMATICA
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Flatten[Table[Sum[Binomial[n, k+m]*2^(n-k-m), {m, 0, n}], {n, 0, 10}, {k, 0, n}]]
More terms from Ross La Haye (rlahaye(AT)new.rr.com), Dec 31 2006
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CROSSREFS
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Row sums = n*3^(n-1) + 3^n = A006234(n+3) (Frank Ruskey and class); a(n, 0) = A000244(n); a(n, 1) = A001047(n); a(n, 2) = A066810(n); A038207.
Sequence in context: A091579 A136159 A005533 this_sequence A050155 A140714 A112932
Adjacent sequences: A112623 A112624 A112625 this_sequence A112627 A112628 A112629
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KEYWORD
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nonn,tabl
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AUTHOR
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Ross La Haye (rlahaye(AT)new.rr.com), Dec 26 2005
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