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%I A137299 #19 Nov 14 2023 17:04:58
%S A137299 3,9,7,31,1,15,97,159,6,1,306,2,3,1,292,961,50,2,7,2,1,3020,2,1,3,1,
%T A137299 47,1,9488,3,1,4,1,13,1,1,29809,1,2,1,60,16539,2,8,2,93648,10,1,2,3,1,
%U A137299 1,1,1,1,294204,21,14,7,3,9,4,6,3,1,3,924269,55,15,1,1,2,1,23,7,1,2,1
%N A137299 Square matrix read by antidiagonals: T(m,n) = m-th term in the continued fraction expansion of Pi^n.
%C A137299 The sequence was suggested by _Leroy Quet_.
%H A137299 Paolo Xausa, <a href="/A137299/b137299.txt">Table of n, a(n) for n = 1..11325</a> (antidiagonals 1..150 of the array, flattened)
%H A137299 J. S. Markovitch, <a href="https://web-archive.southampton.ac.uk/cogprints.org/3667/">Coincidence, data compression and Mach's concept of "economy of thought"</a>, APRI-PH-2004-12b, June 3 2004.
%e A137299 The matrix limited to order 10 is given by matrix(10,10,m,n,contfrac(Pi^n)[m]):
%e A137299 [   3   9   31    97   306   961  3020  9488 29809 93648]
%e A137299 [   7   1  159     2    50     2     3     1    10    21]
%e A137299 [  15   6    3     2     1     1     2     1    14    15]
%e A137299 [   1   1    7     3     4     1     2     7     1     1]
%e A137299 [ 292   2    1     1    60     3     3     1     9     4]
%e A137299 [   1  47   13 16539     1     9     2     1     3     2]
%e A137299 [   1   1    2     1     4     1    10     3     1     1]
%e A137299 [   1   8    1     6    23     5     4     1     5     3]
%e A137299 [   2   1    3     7     1     1     1     1     8     2]
%e A137299 [   1   1    1     6     2     3     1     1    16     1]
%t A137299 A137299list[dmax_]:=With[{a=Array[ContinuedFraction[Pi^(dmax+1-#),#]&,dmax]},Array[Diagonal[a,#]&,dmax,1-dmax]];A137299list[10] (* Generates 10 antidiagonals *) (* _Paolo Xausa_, Nov 14 2023 *)
%o A137299 (PARI) concat(vector(20,i,vector(i,j,contfrac(Pi^(i-j+1))[j])))
%o A137299 (PARI) T(m,n)=contfrac(Pi^n)[m]
%Y A137299 Cf. A001203, A001672, A138324.
%K A137299 nonn,easy,tabl
%O A137299 1,1
%A A137299 _M. F. Hasler_, Mar 14 2008

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