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%I #9 Aug 09 2013 16:15:30
%S -1,1,1,-1,2,-1,1,1,1,1,-1,2,2,2,-1,1,1,4,4,1,1,-1,2,5,8,5,2,-1,1,1,7,
%T 13,13,7,1,1,-1,2,8,20,26,20,8,2,-1,1,1,10,28,46,46,28,10,1,1,-1,2,11,
%U 38,74,92,74,38,11,2,-1,1,1,13,49,112,166,166,112
%N A triangle formed like Pascal's triangle, but with (-1)^(n+1) on the borders instead of 1.
%C This sequence is almost the same as A026637.
%C T(n,k) = A026637(n-2,k-1) for n > 3, 1 < k < n-1. - _Reinhard Zumkeller_, Aug 08 2013
%H T. D. Noe, <a href="/A228053/b228053.txt">Rows n = 0..50 of triangle, flattened</a>
%e Example:
%e -1,
%e 1, 1,
%e -1, 2, -1,
%e 1, 1, 1, 1,
%e -1, 2, 2, 2, -1,
%e 1, 1, 4, 4, 1, 1,
%e -1, 2, 5, 8, 5, 2, -1,
%e 1, 1, 7, 13, 13, 7, 1, 1,
%e -1, 2, 8, 20, 26, 20, 8, 2, -1,
%e 1, 1, 10, 28, 46, 46, 28, 10, 1, 1,
%e -1, 2, 11, 38, 74, 92, 74, 38, 11, 2, -1
%t t = {}; Do[r = {}; Do[If[k == 0 || k == n, m = (-1)^(n+1), m = t[[n, k]] + t[[n, k + 1]]]; r = AppendTo[r, m], {k, 0, n}]; AppendTo[t, r], {n, 0, 10}]; t = Flatten[t]
%o (Haskell)
%o a228053 n k = a228053_tabl !! n !! k
%o a228053_row n = a228053_tabl !! n
%o a228053_tabl = iterate (\row@(i:_) -> zipWith (+)
%o ([- i] ++ tail row ++ [0]) ([0] ++ init row ++ [- i])) [- 1]
%o -- _Reinhard Zumkeller_, Aug 08 2013
%Y Cf. A007318 (Pascal's triangle), A026637 (many terms in common).
%Y Cf. A051601 (n on the borders), A137688 (2^n on borders).
%Y Cf. A097073 (row sums).
%Y Cf. A227074 (4^n edges), A227075 (3^n edges), A227076 (5^n edges).
%K sign,tabl
%O 0,5
%A _T. D. Noe_, Aug 07 2013
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