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A133821
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Triangle whose rows are sequences of increasing fourth powers: 1; 1,16; 1,16,81; ... .
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3
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1, 1, 16, 1, 16, 81, 1, 16, 81, 256, 1, 16, 81, 256, 625, 1, 16, 81, 256, 625, 1296, 1, 16, 81, 256, 625, 1296, 2401, 1, 16, 81, 256, 625, 1296, 2401, 4096, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 10000
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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 1,1,16,1,16,81,1,16,81,256,..., analogous to A002260.
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LINKS
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FORMULA
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O.g.f.: (1+11qx+11q^2x^2+q^3x^3)/((1-x)(1-qx)^5) = 1 + x(1 + 16q) + x^2(1 + 16q + 81q^2) + ... . Cf. 4th row of A008292.
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EXAMPLE
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Triangle starts
1;
1, 16;
1, 16; 81;
1, 16, 81, 256;
1, 16, 81, 256, 625;
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MATHEMATICA
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Module[{nn=10, fp}, fp=Range[(nn(nn+1))/2]^4; Table[TakeList[fp, {n}], {n, nn}]]//Flatten (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Mar 29 2020 *)
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PROG
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(Haskell)
a133821 n k = a133821_tabl !! (n-1) !! (k-1)
a133821_row n = a133821_tabl !! (n-1)
a133821_tabl = map (`take` (tail a000583_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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