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Search: id:A133825
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| A133825 |
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Triangle whose rows are sequences of increasing and decreasing triangular numbers: 1; 1,3,1; 1,3,6,3,1; ... . |
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+0
3
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| 1, 1, 3, 1, 1, 3, 6, 3, 1, 1, 3, 6, 10, 6, 3, 1, 1, 3, 6, 10, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 36, 28, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10, 15, 21, 28, 36, 45, 36, 28, 21, 15, 10, 6, 3, 1, 1, 3, 6, 10
(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 1,1,3,1,1,3,6,3,1,..., analogous to the Smarandache crescendo pyramidal sequence A004737.
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FORMULA
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O.g.f.: (1+qx)/((1-x)(1-qx)^2(1-q^2x)) = 1 + x(1 + 3q + q^2) + x^2(1 + 3q + 6q^2 + 3q^3 + q^4) + ... .
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EXAMPLE
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Triangle starts
1;
1, 3, 1;
1, 3, 6, 3, 1;
1, 3, 6, 10, 6, 3, 1;
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CROSSREFS
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Cf. A000330 (row sums), A004737, A124258, A133826.
Sequence in context: A079650 A094644 A113046 this_sequence A114588 A121745 A089312
Adjacent sequences: A133822 A133823 A133824 this_sequence A133826 A133827 A133828
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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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