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Search: id:A133826
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| A133826 |
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Triangle whose rows are sequences of increasing and decreasing tetrahedral numbers: 1; 1,4,1; 1,4,10,4,1; ... . |
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+0
2
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| 1, 1, 4, 1, 1, 4, 10, 4, 1, 1, 4, 10, 20, 10, 4, 1, 1, 4, 10, 20, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 120, 84, 56, 35, 20, 10, 4, 1, 1, 4, 10, 20, 35, 56, 84, 120, 165, 120, 84, 56, 35, 20
(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 1,1,4,1,1,4,10,4,1,..., 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)^3(1-q^2x)) = 1 + x(1 + 4q + q^2) + x^2(1 + 4q + 10q^2 + 4q^3 + q^4) + ... .
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EXAMPLE
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Triangle starts
1;
1, 4, 1;
1, 4, 10, 4, 1;
1, 4, 10, 20, 10, 4, 1;
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CROSSREFS
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Cf. A000292, A002415 (row sums), A004737, A124258, A133825.
Sequence in context: A080061 A124258 A001638 this_sequence A122185 A136680 A035589
Adjacent sequences: A133823 A133824 A133825 this_sequence A133827 A133828 A133829
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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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