A153860 - OEIS

%I #8 Feb 08 2022 23:20:16

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

%C As an infinite lower triangular matrix M; M * [1,2,3,...] = A063210: (1, 2, 6, 6, 10, 10, 14, 14, ...

%C M * [1, 3, 5, 7, ...] = A047471, {1,3} mod 8. Eigensequence of the triangle = A066983 starting (1, 1, 3, 3, 7, 9, 17, 25, ...).

%C Binomial transform of the triangle = A153861. Row sums = A153284: (1, 1, 3, 1, 3, 1, 3, 1, ...).

%H Reinhard Zumkeller, <a href="/A153860/b153860.txt">Rows n = 1..100 of triangle, flattened</a>

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

%e First few rows of the triangle:

%e    1;

%e    0, 1;

%e    1, 1, 1;

%e   -1, 0, 1, 1;

%e    1, 0, 0, 1, 1;

%e   -1, 0, 0, 0, 1, 1;

%e    1, 0, 0, 0, 0, 1, 1;

%e   -1, 0, 0, 0, 0, 0, 1, 1;

%e    1, 0, 0, 0, 0, 0, 0, 1, 1;

%e   ...

%o (Haskell)

%o a153860 n k = a153860_tabl !! (n-1) !! (k-1)

%o a153860_row n = a153860_tabl !! (n-1)

%o a153860_tabl = [1] : [0, 1] : iterate (\(x:xs) -> -x : 0 : xs) [1, 1, 1]

%o -- _Reinhard Zumkeller_, Dec 16 2013

%Y Cf. A153860, A153284, A063210, A047471.

%K tabl,sign

%O 1,1

%A _Gary W. Adamson_, Jan 03 2009