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 A104509 Matrix inverse of triangle A104505, which is the right-hand side of triangle A084610 of coefficients in (1+x-x^2)^n. 6
 1, 1, -1, 3, -2, 1, 4, -6, 3, -1, 7, -12, 10, -4, 1, 11, -25, 25, -15, 5, -1, 18, -48, 60, -44, 21, -6, 1, 29, -91, 133, -119, 70, -28, 7, -1, 47, -168, 284, -296, 210, -104, 36, -8, 1, 76, -306, 585, -699, 576, -342, 147, -45, 9, -1, 123, -550, 1175, -1580, 1485, -1022, 525, -200, 55, -10, 1, 199, -979, 2310, -3454, 3641 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Leftmost column is A000204 (Lucas numbers). Other columns include: A045925, A067988. Row sums are: {1,0,2,0,2,0,2,...}. Absolute row sums form: A099425. Antidiagonal sums are: {1,1,2,2,2,2,2,...}. Absolute antidiagonal sums are: A084214. Riordan array ( (1 + x^2/(1 - x - x^2), -x/(1 - x - x^2) ) belonging to the hitting time subgroup of the Riordan group (see Peart and Woan). - Peter Bala, Jun 29 2015 LINKS Robert Israel, Table of n, a(n) for n = 0..10152 (rows 0 to 141, flattened). P. Peart and W.-J. Woan, A divisibility property for a subgroup of Riordan matrices, Discrete Applied Mathematics, Vol. 98, Issue 3, Jan 2000, 255-263. FORMULA G.f.: A(x, y) = (1 + x^2)/(1-x-x^2 + x*y). G.f. for column k: g_k(x) = -(x^2+1)*x^k/(x^2+x-1)^(k+1). - Robert Israel, Jun 30 2015 EXAMPLE Rows begin: 1; 1,-1; 3,-2,1; 4,-6,3,-1; 7,-12,10,-4,1; 11,-25,25,-15,5,-1; 18,-48,60,-44,21,-6,1; 29,-91,133,-119,70,-28,7,-1; 47,-168,284,-296,210,-104,36,-8,1; 76,-306,585,-699,576,-342,147,-45,9,-1; ... MAPLE S:= series((1 + x^2)/(1-x-x^2 + x*y), x, 20): for n from 0 to 19 do R[n]:= coeff(S, x, n) od: seq(seq(coeff(R[n], y, j), j=0..n), n=0..19); # Robert Israel, Jun 30 2015 MATHEMATICA nmax = 11; T[n_, k_] := Coefficient[(1 + x - x^2)^n, x, n + k]; M = Table[T[n, k], {n, 0, nmax}, {k, 0, nmax}] // Inverse; Table[M[[n+1, k+1]], {n, 0, nmax}, {k, 0, n}] // Flatten (* Jean-François Alcover, Mar 27 2019 *) PROG (PARI) {T(n, k)=local(X=x+x*O(x^n), Y=y+y*O(y^k)); polcoeff(polcoeff((1 + X^2)/(1-X-X^2 + X*Y), n, x), k, y)} (PARI) tabl(nn) = {my(m = matrix(nn, nn, n, k, n--; k--; if((n

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)