A109248 -id:A109248 - cp's OEIS frontend

A109246 Riordan array (1-x-2x^2,x(1-x)).

1, -1, 1, -2, -2, 1, 0, -1, -3, 1, 0, 2, 1, -4, 1, 0, 0, 3, 4, -5, 1, 0, 0, -2, 2, 8, -6, 1, 0, 0, 0, -5, -2, 13, -7, 1, 0, 0, 0, 2, -7, -10, 19, -8, 1, 0, 0, 0, 0, 7, -5, -23, 26, -9, 1, 0, 0, 0, 0, -2, 14, 5, -42, 34, -10, 1, 0, 0, 0, 0, 0, -9, 19, 28, -68, 43, -11, 1, 0, 0, 0, 0, 0, 2, -23, 14, 70, -102, 53, -12, 1, 0, 0, 0, 0, 0, 0, 11, -42, -14

Offset: 0

Paul Barry, Jun 23 2005

Matrix inverse of A109244. Row sums are A109247. Diagonal sums are A109248.

			Rows begin
1;
-1,1;
-2,-2,1;
0,-1,-3,1;
0,2,1,-4,1;
0,0,3,4,-5,1

A117363 Expansion of (1-2x)/(1-x^2+x^3).

Original entry on oeis.org

1, -2, 1, -3, 3, -4, 6, -7, 10, -13, 17, -23, 30, -40, 53, -70, 93, -123, 163, -216, 286, -379, 502, -665, 881, -1167, 1546, -2048, 2713, -3594, 4761, -6307, 8355, -11068, 14662, -19423, 25730, -34085, 45153, -59815, 79238

Offset: 0

Paul Barry, Mar 10 2006

Diagonal sums of number triangle A117362.

Index entries for linear recurrences with constant coefficients, signature (0,1,-1).

Cf. A109248, A007307.

CoefficientList[Series[(1-2x)/(1-x^2+x^3),{x,0,60}],x] (* or *) LinearRecurrence[ {0,1,-1},{1,-2,1},60] (* Harvey P. Dale, Aug 04 2021 *)

a(n)=a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), (-1)^n*(C(k,n-2k)+2*C(k,n-2k-1))}.

cp's OEIS Frontend

A109246 Riordan array (1-x-2x^2,x(1-x)).

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A117363 Expansion of (1-2x)/(1-x^2+x^3).

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