A174015 -id:A174015 - cp's OEIS frontend

A174014 Deleham triangle [1,1,-1,1,1,-1,1,...] DELTA [1,0,0,1,0,0,1,0,...], DELTA defined in A084938.

1, 1, 1, 2, 3, 1, 3, 7, 5, 1, 4, 13, 15, 7, 1, 4, 19, 33, 26, 9, 1, 2, 19, 53, 66, 40, 11, 1, -3, 3, 51, 115, 115, 57, 13, 1, -10, -37, -19, 103, 215, 183, 77, 15, 1, -14, -89, -193, -120, 173, 364, 273, 100, 17, 1, -4, -91, -387, -664, -406, 252, 574, 388, 126, 19, 1

Offset: 0

Paul Barry, Mar 05 2010

First column is A174015. Row sums are A174016. Diagonal sums are A174013.

			Triangle begins
1,
1, 1,
2, 3, 1,
3, 7, 5, 1,
4, 13, 15, 7, 1,
4, 19, 33, 26, 9, 1,
2, 19, 53, 66, 40, 11, 1,
-3, 3, 51, 115, 115, 57, 13, 1,
-10, -37, -19, 103, 215, 183, 77, 15, 1,
-14, -89, -193, -120, 173, 364, 273, 100, 17, 1

A198379 Triangle T(n,k), read by rows, given by (0,1,-1,0,1,-1,0,1,-1,0,1,-1,...) DELTA (1,0,0,1,0,0,1,0,0,1,0,0,1,...) where DELTA is the operator defined in A084938.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 0, 3, 1, 0, 0, -1, 0, 4, 1, 0, 0, 0, -4, 0, 5, 1, 0, 0, 0, 0, -10, 0, 6, 1, 0, 0, 0, 2, 0, -20, 0, 7, 1, 0, 0, 0, 0, 12, 0, -35, 0, 8, 1, 0, 0, 0, 0, 0, 42, 0, -56, 0, 9, 1

Offset: 0

Philippe Deléham, Oct 28 2011

Equal to A174014*A130595 as infinite lower triangular matrices.

			Triangle begins :
1
0, 1
0, 1, 1
0, 0, 2, 1
0, 0, 0, 3, 1
0, 0, -1, 0, 4, 1
0, 0, 0, -4, 0, 5, 1
0, 0, 0, 0, -10, 0, 6, 1

Cf. A174014, A174015, A174016

Sum_k>=0 T(n,k)= A174015(n).
Sum_k>=0 T(n,k)*2^k = A174016(n).
Sum_ {0<=k<=n} T(n,k)*(-1)^(n-k) = A168505(n).

cp's OEIS Frontend

A174014 Deleham triangle [1,1,-1,1,1,-1,1,...] DELTA [1,0,0,1,0,0,1,0,...], DELTA defined in A084938.

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