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A238988
Triangle T(n,k), read by rows, given by (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.
1
1, 1, 1, 0, 1, 1, -1, 0, 2, 1, -1, -1, 1, 2, 1, 0, -1, -2, 1, 3, 1, 1, 0, -4, -2, 3, 3, 1, 1, 1, -2, -4, -2, 3, 4, 1, 0, 1, 3, -2, -9, -2, 6, 4, 1, -1, 0, 6, 3, -9, -9, 0, 6, 5, 1, -1, -1, 3, 6, 3, -9, -15, 0, 10, 5, 1, 0, -1, -4, 3, 18, 3, -24, -15, 5, 10, 6, 1
OFFSET
0,9
COMMENTS
T(n,0) = T(n+1,1) = A010892(n), T(n+2,2) = T(n+3,3) = A099254(n), T(n+4,4) = T(n+5,5) = A128504(n).
Triangle T(n,k) = A101950(n - floor((k+1)/2),floor(k/2)).
LINKS
Indranil Ghosh, Rows 0..100, flattened
FORMULA
G.f.: (1 + x*y)/(1 - x + x^2 - x^2*y^2).
T(n,k) = T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n.
Sum_{k = 0..n} T(n,k)*x^k = A000007(n), A010892(n), A040000(n), A105476(n+1) for x = -1, 0, 1, 2 respectively.
EXAMPLE
Triangle begins:
1;
1, 1;
0, 1, 1;
-1, 0, 2, 1;
-1, -1, 1, 2, 1;
0, -1, -2, 1, 3, 1;
1, 0, -4, -2, 3, 3, 1;
1, 1, -2, -4, -2, 3, 4, 1;
0, 1, 3, -2, -9, -2, 6, 4, 1;
-1, 0, 6, 3, -9, -9, 0, 6, 5, 1;
-1, -1, 3, 6, 3, -9, -15, 0, 10, 5, 1;
0, -1, -4, 3, 18, 3, -24, -15, 5, 10, 6, 1;
1, 0, -8, -4, 18, 18, -6, -24, -20, 5, 15, 6, 1;
MATHEMATICA
nmax=11; Flatten[CoefficientList[Series[CoefficientList[Series[(1 + x*y)/(1 - x + x^2 - x^2*y^2), {x, 0, nmax}], x], {y, 0, nmax}], y]] (* Indranil Ghosh, Mar 14 2017 *)
CROSSREFS
Sequence in context: A343776 A328384 A016024 * A261013 A335106 A093518
KEYWORD
easy,sign,tabl
AUTHOR
Philippe Deléham, Mar 07 2014
STATUS
approved