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 A202209 Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 1
 1, 2, 0, 5, 1, 0, 13, 5, 0, 0, 34, 19, 1, 0, 0, 89, 65, 8, 0, 0, 0, 233, 210, 42, 1, 0, 0, 0, 610, 654, 183, 11, 0, 0, 0, 0, 1597, 1985, 717, 74, 1, 0, 0, 0, 0, 4181, 5911, 2622, 394, 14, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Riordan array ((1-x)/(1-3x+x^2), x^2/(1-3x+x^2)) . LINKS Table of n, a(n) for n=0..54. FORMULA T(n,k) = 3*T(n-1,k) - T(n-2,k) + T(n-2,k-1). G.f.: (1-x)/(1-3x+(1-y)*x^2). Sum_{k, 0<=k<=n} T(n,k)*x^k = A057682(n+1), A000079(n), A122367(n), A025192(n), A052924(n), A104934(n), A202206(n), A122117(n), A197189(n) for x = -2, -1, 0, 1, 2, 3, 4, 5, 6 respectively. T(n,0) = A122367(n) = A000045(2n+1). EXAMPLE Triangle begins : 1 2, 0 5, 1, 0 13, 5, 0, 0 34, 19, 1, 0, 0 89, 65, 8, 0, 0, 0 233, 210, 42, 1, 0, 0, 0 CROSSREFS Cf. A000045, A000079, A001519, A001870, A001906, A126124, A202207 (antidiagonal sums) Sequence in context: A261044 A117780 A155759 * A201730 A188449 A177267 Adjacent sequences: A202206 A202207 A202208 * A202210 A202211 A202212 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Dec 14 2011 STATUS approved

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Last modified December 2 09:21 EST 2023. Contains 367516 sequences. (Running on oeis4.)