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 A112883 A skew Jacobsthal-Pascal matrix. 1
 1, 0, 1, 0, 1, 3, 0, 0, 2, 5, 0, 0, 1, 7, 11, 0, 0, 0, 3, 16, 21, 0, 0, 0, 1, 12, 41, 43, 0, 0, 0, 0, 4, 34, 94, 85, 0, 0, 0, 0, 1, 18, 99, 219, 171, 0, 0, 0, 0, 0, 5, 60, 261, 492, 341, 0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683, 0, 0, 0, 0, 0, 0, 6, 95, 576, 1692, 2426, 1365, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS T(n,n) is A001045(n), row sums are A006130, column sums are A002605. Compare with [0,1,-1,0,0,..] DELTA [1,2,-2,0,0,...] where DELTA is the operator defined in A084938. A skewed version of the Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)) (A073370). Modulo 2, this sequence gives A106344. - Philippe Deléham, Dec 18 2008 LINKS Table of n, a(n) for n=0..82. FORMULA From Philippe Deléham: (Start) G.f.: 1/(1-yx(1-x)-2x^2*y*2); Number triangle T(n, k) = Sum_{j=0..2k-n} C(n-k+j, n-k)*C(j, 2k-n-j)*2^(2k-n-j); T(n, k) = A073370(k, n-k); T(n, k) = T(n-1, k-1) + T(n-2, k-1) + 2*T(n-2, k-2). (End) EXAMPLE Rows begin 1; 0, 1; 0, 1, 3; 0, 0, 2, 5; 0, 0, 1, 7, 11; 0, 0, 0, 3, 16, 21; 0, 0, 0, 1, 12, 41, 43; 0, 0, 0, 0, 4, 34, 94, 85; 0, 0, 0, 0, 1, 18, 99, 219, 171; 0, 0, 0, 0, 0, 5, 60, 261, 492, 341; 0, 0, 0, 0, 0, 1, 25, 195, 678, 1101, 683; CROSSREFS Cf. A111006. Sequence in context: A357317 A357236 A156548 * A117138 A292255 A362313 Adjacent sequences: A112880 A112881 A112882 * A112884 A112885 A112886 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Oct 05 2005 STATUS approved

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Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)