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 A206474 Riordan array ((1+x-x^2)/(1-x^2), x/(1-x^2)). 1
 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 3, 3, 1, 1, 0, 3, 3, 4, 4, 1, 1, 1, 1, 6, 6, 5, 5, 1, 1, 0, 4, 4, 10, 10, 6, 6, 1, 1, 1, 1, 10, 10, 15, 15, 7, 7, 1, 1, 0, 5, 5, 20, 20, 21, 21, 8, 8, 1, 1, 1, 1, 15, 15, 35, 35, 28, 28, 9, 9, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS Triangle T(n,k), read by rows, given by (1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Antidiagonal sums are A158780(n+1). Row sums are 2*Fibonacci(n) = 2*A000045(n), n>0. LINKS Table of n, a(n) for n=0..77. FORMULA T(2n, 2k) = A128908(n,k), T(2n+1, 2k) = T(2n+1, 2k+1) = A085478(n,k) = Binomial (n+k, 2k), T(2n+2, 2k+1) = A078812(n,k) = Binomial(n+k-1, 2k-1). T(n,k) = T(n-1,k-1) + T(n-2,k), T(0,0) = T(0,1) = 1, T(0,2) = 0. G.f.: (1+x-x^2)/(1-x*y-x^2). Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n* A000129(n) (n>0), A000007(n), A135528(n-1), A055389(n) for x = -2, -1, 0, 1 respectively . EXAMPLE Triangle begins : 1 1, 1 0, 1, 1 1, 1, 1, 1 0, 2, 2, 1, 1 1, 1, 3, 3, 1, 1 0, 3, 3, 4, 4, 1, 1 1, 1, 6, 6, 5, 5, 1, 1 0, 4, 4, 10, 10, 6, 6, 1, 1 1, 1, 10, 10, 15, 15, 7, 7, 1, 1 0, 5, 5, 20, 20, 21, 21, 8, 8, 1, 1 1, 1, 15, 15, 35, 35, 28, 28, 9, 9, 1, 1 MATHEMATICA t[1, 0] = 1; t[2, 0] = 0; t[n_, n_] = 1; t[n_ /; n >= 0, k_ /; k >= 0] /; k <= n := t[n, k] = t[n-1, k-1] + t[n-2, k]; t[n_, k_] = 0; Table[t[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 28 2013 *) CROSSREFS Cf. A007318, A078812, A085478, A128908, Sequence in context: A286634 A099245 A185331 * A211999 A175025 A076899 Adjacent sequences: A206471 A206472 A206473 * A206475 A206476 A206477 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 08 2012 STATUS approved

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Last modified December 7 05:10 EST 2023. Contains 367629 sequences. (Running on oeis4.)