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%I #44 Sep 08 2022 08:46:03
%S 0,1,0,1,1,0,9,3,3,0,1,3,1,1,0,25,5,15,5,5,0,9,15,3,9,3,3,0,49,21,35,
%T 7,21,7,7,0,4,14,6,10,2,6,2,2,0,81,18,63,27,45,9,27,9,9,0,25,45,10,35,
%U 15,25,5,15,5,5,0,121,55,99,22,77,33,55,11,33,11,11,0,9,33,15,27,6,21,9,15,3,9,3,3,0
%N Array t(n,k) of the family ((n+k)/gcd(n+k,4))*(n/gcd(n,4)), read by antidiagonals.
%C Identification of rows and columns:
%C Row 2, n=1: A060819,
%C row 3, n=2: A060819 (shifted),
%C row 4, n=3: A068219,
%C row 5, n=4: A060819 (shifted),
%C row 6, n=5: A060819 (shifted and multiplied by 5),
%C row 7, n=6: A068219 (shifted),
%C row 8, n=7: A060819 (shifted and multiplied by 7);
%C column 1, k=0: A181318,
%C column 2, k=1: A064038,
%C column 3, k=2: A198148,
%C column 4, k=3: A160050,
%C column 5, k=4: A061037,
%C column 6, k=5: A178242,
%C column 7, k=6: A217366,
%C column 8, k=7: A217367.
%C This array is the transposition of the array given by _Paul Curtz_ in the comments in A181318.
%H G. C. Greubel, <a href="/A215189/b215189.txt">Antidiagonals n=0..100 of triangle, flattened</a>
%F t(n,k) = ((n+k)/gcd(n+k,4))*(n/gcd(n,4)).
%e Array begins:
%e 0, 0, 0, 0, 0, 0, 0, ...
%e 1, 1, 3, 1, 5, 3, 7, ...
%e 1, 3, 1, 5, 3, 7, 2, ...
%e 9, 3, 15, 9, 21, 6, 27, ...
%e 1, 5, 3, 7, 2, 9, 5, ...
%e 25, 15, 35, 10, 45, 25, 55, ...
%e 9, 21, 6, 27, 15, 33, 9, ...
%e 49, 14, 63, 35, 77, 21, 91, ...
%e ...
%e Triangle begins:
%e 0;
%e 1, 0;
%e 1, 1, 0;
%e 9, 3, 3, 0;
%e 1, 3, 1, 1, 0;
%e 25, 5, 15, 5, 5, 0;
%e 9, 15, 3, 9, 3, 3, 0;
%e 49, 21, 35, 7, 21, 7, 7, 0;
%e 4, 14, 6, 10, 2, 6, 2, 2, 0;
%e 81, 18, 63, 27, 45, 9, 27, 9, 9, 0;
%e 25, 45, 10, 35, 15, 25, 5, 15, 5, 5, 0;
%e 121, 55, 99, 22, 77, 33, 55, 11, 33, 11, 11, 0;
%e 9, 33, 15, 27, 6, 21, 9, 15, 3, 9, 3, 3, 0;
%e ...
%t t[n_, k_] := (n+k)/GCD[n+k, 4]*n/GCD[n, 4]; Table[t[n-k, k], {n, 0, 12}, {k, 0, n}] // Flatten
%o (Magma) /* As triangle: */ [[(n-k)/GCD(n-k, 4)*n/GCD(n, 4): k in [0..n]]: n in [0..12]]; // _Bruno Berselli_, Jun 13 2013
%Y Cf. A060819, A181318, A064038, A198148, A160050, A061037, A178242, A217366, A217367.
%K nonn,tabl
%O 0,7
%A _Jean-François Alcover_, Jun 12 2013
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