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Search: id:A133819
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| A133819 |
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Triangle whose rows are sequences of increasing squares: 1; 1,4; 1,4,9; ... . |
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+0
10
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| 1, 1, 4, 1, 4, 9, 1, 4, 9, 16, 1, 4, 9, 16, 25, 1, 4, 9, 16, 25, 36, 1, 4, 9, 16, 25, 36, 49, 1, 4, 9, 16, 25, 36, 49, 64, 1, 4, 9, 16, 25, 36, 49, 64, 81, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
(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 1,1,4,1,4,9,1,4,9,16,..., analogous to the Smarandache crescendo sequence A002260.
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REFERENCES
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(Bernard) de? Frenicle (de Bessy), studying Pythagorean triangles: Methode pour trouver .., p. 11; in Divers ouvrages de mathematique et de physique par Messieurs de l'Academie Royale des Sciences, In-folio, (4)+6+519 pages, Paris, 1693. - Paul Curtz (bpcrtz(AT)free.fr), Aug 18 2008
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FORMULA
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O.g.f.: (1+qx)/((1-x)(1-qx)^3) = 1 + x(1 + 4q) + x^2(1 + 4q + 9q^2) + ... .
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EXAMPLE
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Triangle starts
1;
1, 4;
1, 4, 9;
1, 4, 9, 16;
1, 4, 9, 16, 25;
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CROSSREFS
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Sequence in context: A131112 A141225 A079185 this_sequence A021245 A007891 A165487
Adjacent sequences: A133816 A133817 A133818 this_sequence A133820 A133821 A133822
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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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