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Search: id:A124258
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| A124258 |
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Triangle whose rows are sequences of increasing and decreasing squares: 1; 1,4,1; 1,4,9,4,1; ... |
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+0
6
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| 1, 1, 4, 1, 1, 4, 9, 4, 1, 1, 4, 9, 16, 9, 4, 1, 1, 4, 9, 16, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 64, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 36, 49, 64, 81, 64, 49, 36, 25, 16, 9, 4, 1, 1, 4, 9, 16
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The triangle A003983 with individual entries squared and each 2nd row skipped.
The sequence 1,1,4,1,1,4,9,4,1,..., analogous to the Smarandache crescendo pyramidal sequence A004737. - Peter Bala (pbala(AT)toucansurf.com), Sep 25 2007
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FORMULA
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O.g.f.: (1+qx)^2/((1-x)(1-qx)^2(1-q^2x)) = 1 + x(1 + 4q + q^2) + x^2(1 + 4q + 9q^2 + 4q^3 + q^4) + ... . - Peter Bala (pbala(AT)toucansurf.com), Sep 25 2007
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EXAMPLE
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Triangle starts
1;
1, 4, 1;
1, 4, 9, 4, 1:
1, 4, 9, 16, 9, 4, 1:
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MAPLE
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A003983 := proc(n, k) min(n, k) ; end: A124258 := proc(n, k) A003983(n, k)^2 ; end: for d from 1 to 20 by 2 do for c from 1 to d do printf("%d, ", A124258(d+1-c, c)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 21 2007
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CROSSREFS
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Cf. A005900 (row sums), A004737, A133819, A133823, A133824, A133825.
Sequence in context: A016523 A026998 A080061 this_sequence A001638 A133826 A122185
Adjacent sequences: A124255 A124256 A124257 this_sequence A124259 A124260 A124261
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 16 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 21 2007
Edited by njas, Jun 30 at the suggestion of R. J. Mathar.
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