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 A113953 A Jacobsthal matrix. 2
 1, 0, 1, 0, 2, 1, 0, 0, 4, 1, 0, 0, 4, 6, 1, 0, 0, 0, 12, 8, 1, 0, 0, 0, 8, 24, 10, 1, 0, 0, 0, 0, 32, 40, 12, 1, 0, 0, 0, 0, 16, 80, 60, 14, 1, 0, 0, 0, 0, 0, 80, 160, 84, 16, 1, 0, 0, 0, 0, 0, 32, 240, 280, 112, 18, 1, 0, 0, 0, 0, 0, 0, 192, 560, 448, 144, 20, 1, 0, 0, 0, 0, 0, 0, 64, 672 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Rows sums are the Jacobsthal numbers A001045(n+1). Diagonal sums are the Padovan-Jacobsthal numbers A052947. Inverse is (1,xc(-2x)), c(x) the g.f. of A000108, with general term k*C(2n-k-1,n-k)(-2)^(n - k)/n. Triangle read by rows given by (0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 01 2013 LINKS FORMULA G.f.: 1/(1-xy(1+2x)). Riordan array (1, x(1+2x)). T(n, k) = 2^(n-k)*binomial(k, n-k). T(n,k) = A026729(n,k)*2^(n-k) . - Philippe Deléham, Nov 22 2006 T(n,k) = T(n-1,k-1) + 2*T(n-2,k-1), T(0,0) = 1, T(n,k) = 0 if k<0 or if k>n. - Philippe Deléham, Nov 01 2013 EXAMPLE Rows begin 1; 0, 1; 0, 2, 1; 0, 0, 4, 1; 0, 0, 4, 6, 1; 0, 0, 0, 12, 8, 1; 0, 0, 0, 8, 24, 10, 1; CROSSREFS A signed version is A110509. Sequence in context: A320531 A065719 A204387 * A110509 A319574 A204040 Adjacent sequences:  A113950 A113951 A113952 * A113954 A113955 A113956 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Nov 09 2005 STATUS approved

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Last modified August 23 00:50 EDT 2019. Contains 326211 sequences. (Running on oeis4.)