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A153860 Triangle by columns: leftmost column = (1, 0, 1, -1, 1, -1, 1, ...); columns >1 = (1, 1, 0, 0, 0, ...).

%I A153860 #13 May 07 2025 08:18:27
%S A153860 1,0,1,1,1,1,-1,0,1,1,1,0,0,1,1,-1,0,0,0,1,1,1,0,0,0,0,1,1,-1,0,0,0,0,
%T A153860 0,1,1,1,0,0,0,0,0,0,1,1,-1,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,1,1
%N A153860 Triangle by columns: leftmost column = (1, 0, 1, -1, 1, -1, 1, ...); columns >1 = (1, 1, 0, 0, 0, ...).
%C A153860 As an infinite lower triangular matrix M; M * [1,2,3,...] = A063210: (1, 2, 6, 6, 10, 10, 14, 14, ...).
%C A153860 M * [1, 3, 5, 7, ...] = A047471, {1,3} mod 8.
%C A153860 Eigensequence of the triangle = A066983 starting (1, 1, 3, 3, 7, 9, 17, 25, ...).
%C A153860 Binomial transform of the triangle = A153861.
%C A153860 Row sums = A153284: (1, 1, 3, 1, 3, 1, 3, 1, ...).
%H A153860 Reinhard Zumkeller, <a href="/A153860/b153860.txt">Rows n = 1..100 of triangle, flattened</a>
%F A153860 Triangle by columns: leftmost column = (1, 0, 1, -1, 1, ...); columns > 1 = (1, 1, 0, 0, 0, ...).
%e A153860 First few rows of the triangle:
%e A153860    1;
%e A153860    0, 1;
%e A153860    1, 1, 1;
%e A153860   -1, 0, 1, 1;
%e A153860    1, 0, 0, 1, 1;
%e A153860   -1, 0, 0, 0, 1, 1;
%e A153860    1, 0, 0, 0, 0, 1, 1;
%e A153860   -1, 0, 0, 0, 0, 0, 1, 1;
%e A153860    1, 0, 0, 0, 0, 0, 0, 1, 1;
%e A153860   ...
%o A153860 (Haskell)
%o A153860 a153860 n k = a153860_tabl !! (n-1) !! (k-1)
%o A153860 a153860_row n = a153860_tabl !! (n-1)
%o A153860 a153860_tabl = [1] : [0, 1] : iterate (\(x:xs) -> -x : 0 : xs) [1, 1, 1]
%o A153860 -- _Reinhard Zumkeller_, Dec 16 2013
%Y A153860 Cf. A153861 (binomial transform), A153284 (row sums), A063210, A047471, A066983.
%K A153860 tabl,sign
%O A153860 1,1
%A A153860 _Gary W. Adamson_, Jan 03 2009