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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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14
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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;
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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Reading the triangle by rows produces the sequence 1,1,4,1,4,9,1,4,9,16,..., analogous to A002260.
Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. A133819 is reluctant sequence of A000290. - Boris Putievskiy, Jan 11 2013
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LINKS
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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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The triangle T(n, k) starts:
1;
1, 4;
1, 4, 9;
1, 4, 9, 16;
1, 4, 9, 16, 25;
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MATHEMATICA
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With[{sqs=Range[12]^2}, Flatten[Table[Take[sqs, n], {n, 12}]]] (* Harvey P. Dale, Sep 09 2012 *)
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PROG
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(Haskell)
a133819 n k = a133819_tabl !! (n-1) !! (k-1)
a133819_row n = a133819_tabl !! (n-1)
a133819_tabl = map (`take` (tail a000290_list)) [1..]
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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