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URL: https://oeis.org/A228053

⇱ A228053 - OEIS

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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
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
EXAMPLE
Triangle begins:
-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
KEYWORD
sign,tabl
AUTHOR
T. D. Noe, Aug 07 2013
STATUS
approved