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%I #13 Sep 23 2021 00:32:45
%S 1,2,3,2,4,7,0,2,2,9,0,0,2,4,13,0,0,0,2,2,15,2,2,2,2,4,6,21,2,0,2,0,2,
%T 2,4,25,2,0,0,2,2,0,2,6,31,0,2,2,2,0,2,2,4,2,33,0,0,2,0,2,2,0,2,2,4,
%U 37,0,0,0,2,2,0,2,2,0,2,6,43,2,2,2,2,0,2
%N Triangle of iterated absolute differences of lucky numbers read by antidiagonals upwards.
%C This sequence is related to the lucky numbers (cf. A000959) in the same way as A036262 is related to the prime numbers;
%C T(n,0) = A054978(n);
%C T(2*n,n) = A254969(n);
%C T(n,n-1) = A031883(n), n > 0;
%C T(n,n) = A000959(n+1);
%C for n > 0: T(n,k) = abs(T(n,k+1) - T(n-1,k), k = 0 .. n-1.
%H Reinhard Zumkeller, <a href="/A254967/b254967.txt">Rows n = 0..125 of triangle, flattened</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LuckyNumber.html">Lucky number.</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucky_number">Lucky number</a>
%e . 0: 1
%e . 1: 2 3
%e . 2: 2 4 7
%e . 3: 0 2 2 9
%e . 4: 0 0 2 4 13
%e . 5: 0 0 0 2 2 15
%e . 6: 2 2 2 2 4 6 21
%e . 7: 2 0 2 0 2 2 4 25
%e . 8: 2 0 0 2 2 0 2 6 31
%e . 9: 0 2 2 2 0 2 2 4 2 33
%e . 10: 0 0 2 0 2 2 0 2 2 4 37
%e . 11: 0 0 0 2 2 0 2 2 0 2 6 43
%e . 12: 2 2 2 2 0 2 2 0 2 2 0 6 49
%e . 13: 0 2 0 2 0 0 2 0 0 2 4 4 2 51 .
%t nmax = 13; (* max index for triangle rows *)
%t imax = 25; (* max index for initial lucky array L *)
%t L = Table[2i + 1, {i, 0, imax}];
%t For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];
%t T[n_, n_] := If[n+1 <= Length[L], L[[n+1]], Print["imax should be increased"]; 0];
%t T[n_, k_] := T[n, k] = Abs[T[n, k+1] - T[n-1, k]];
%t Table[T[n, k], {n, 0, nmax}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Sep 22 2021 *)
%o (Haskell)
%o a254967 n k = a254967_tabl !! n !! k
%o a254967_row n = a254967_tabl !! n
%o a254967_tabl = diags [] $
%o iterate (\lds -> map abs $ zipWith (-) (tail lds) lds) a000959_list
%o where diags uss (vs:vss) = (map head wss) : diags (map tail wss) vss
%o where wss = vs : uss
%Y Cf. A054978 (left edge), A254969 (central terms), A000959 (right edge), A031883, A036262.
%K nonn,tabl
%O 0,2
%A _Reinhard Zumkeller_, Feb 11 2015
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