A202480
Riordan array (1/(1-x), x(2x-1)/(1-x)^2).
Original entry on oeis.org
1, 1, -1, 1, -1, 1, 1, 0, 1, -1, 1, 2, -1, -1, 1, 1, 5, -5, 2, 1, -1, 1, 9, -10, 8, -3, -1, 1, 1, 14, -14, 14, -11, 4, 1, -1, 1, 20, -14, 14, -17, 14, -5, -1, 1, 1, 27, -6, 0, -9, 19, -17, 6, 1, -1
Offset: 0
Triangle begins :
1
1, -1
1, -1, 1
1, 0, 1, -1
1, 2, -1, -1, 1
1, 5, -5, 2, 1, -1
1, 9, -10, 8, -3, -1, 1
1, 14, -14, 14, -11, 4, 1, -1
(1+x^2-x^3)/(1-2x)^3 is the g.f of column A165241(n+2,2) := 1, 6, 25, 85, 258, 728, 1952, 5040, ...
A122788
(1,3)-entry of the 3 X 3 matrix M^n, where M = {{0, -1, 1}, {1, 1, 0}, {0, 1, 1}}.
Original entry on oeis.org
0, 1, 1, 0, 0, 2, 4, 4, 4, 8, 16, 24, 32, 48, 80, 128, 192, 288, 448, 704, 1088, 1664, 2560, 3968, 6144, 9472, 14592, 22528, 34816, 53760, 82944, 128000, 197632, 305152, 471040, 727040, 1122304, 1732608, 2674688, 4128768, 6373376, 9838592, 15187968, 23445504
Offset: 0
a(7)=4 because M^7 = {{0,4,4},{4,4,8},{8,12,12}}.
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with(linalg): M[1]:=matrix(3,3,[0,-1,1,1,1,0,0,1,1]): for n from 2 to 42 do M[n]:=multiply(M[1],M[n-1]) od: 0,seq(M[n][1,3],n=1..42);
a[0]:=0: a[1]:=1: a[2]:=1: for n from 3 to 42 do a[n]:=2*a[n-1]-2*a[n-2]+2*a[n-3] od: seq(a[n],n=0..42);
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M = {{0, -1, 1}, {1, 1, 0}, {0, 1, 1}}; v[1] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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concat(0, Vec(x*(1 - x) / (1 - 2*x + 2*x^2 - 2*x^3) + O(x^50))) \\ Colin Barker, Mar 03 2017
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