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Search: id:A133823
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| A133823 |
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Triangle whose rows are sequences of increasing and decreasing cubes:1; 1,8,1; 1,8,27,8,1; ... . |
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+0
4
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| 1, 1, 8, 1, 1, 8, 27, 8, 1, 1, 8, 27, 64, 27, 8, 1, 1, 8, 27, 64, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 512, 343, 216, 125, 64, 27, 8, 1, 1, 8, 27, 64, 125, 216, 343, 512, 729
(list; table; graph; listen)
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OFFSET
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0,3
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COMMENT
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Reading the triangle by rows produces the sequence 1,1,8,1,1,8,27,8,1,..., analogous to the Smarandache crescendo pyramidal sequence A004737.
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FORMULA
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O.g.f.: (1+qx)(1+4qx+q^2x^2)/((1-x)(1-qx)^3(1-q^2x)) = 1 + x(1 + 8q + q^2) + x^2(1 + 8q + 27q^2 + 8q^3 + q^4) + ... .
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EXAMPLE
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Triangle starts
1;
1, 8, 1;
1, 8, 27, 8, 1;
1, 8, 27, 64, 27, 8, 1;
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CROSSREFS
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Cf. A004737, A037270 (row sums), A133820, A124258, A133824.
Sequence in context: A010151 A021556 A109571 this_sequence A146881 A131067 A143679
Adjacent sequences: A133820 A133821 A133822 this_sequence A133824 A133825 A133826
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Peter Bala (pbala(AT)toucansurf.com), Sep 25 2007
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