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 A228053 A triangle formed like Pascal's triangle, but with (-1)^(n+1) on the borders instead of 1. 6
 -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, 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, 38, 74, 92, 74, 38, 11, 2, -1, 1, 1, 13, 49, 112, 166, 166, 112 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS This sequence is almost the same as A026637. T(n,k) = A026637(n-2,k-1) for n > 3, 1 < k < n-1. - Reinhard Zumkeller, Aug 08 2013 LINKS T. D. Noe, Rows n = 0..50 of triangle, flattened EXAMPLE Example: -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, 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, 38, 74, 92, 74, 38, 11, 2, -1 MATHEMATICA 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] PROG (Haskell) a228053 n k = a228053_tabl !! n !! k a228053_row n = a228053_tabl !! n a228053_tabl = iterate (\row@(i:_) -> zipWith (+)    ([- i] ++ tail row ++ [0]) ([0] ++ init row ++ [- i])) [- 1]   -- Reinhard Zumkeller, Aug 08 2013 CROSSREFS Cf. A007318 (Pascal's triangle), A026637 (many terms in common). Cf. A051601 (n on the borders), A137688 (2^n on borders). Cf. A097073 (row sums). Cf. A227074 (4^n edges), A227075 (3^n edges), A227076 (5^n edges). Sequence in context: A127836 A307433 A245618 * A031262 A047072 A178058 Adjacent sequences:  A228050 A228051 A228052 * A228054 A228055 A228056 KEYWORD sign,tabl AUTHOR T. D. Noe, Aug 07 2013 STATUS approved

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)