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 A202390 Triangle T(n,k), read by rows, given by (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 4
 1, 1, 1, 1, 3, 2, 1, 6, 8, 3, 1, 10, 21, 17, 5, 1, 15, 45, 58, 35, 8, 1, 21, 85, 154, 144, 68, 13, 1, 28, 147, 350, 452, 330, 129, 21, 1, 36, 238, 714, 1195, 1198, 719, 239, 34, 1, 45, 366, 1344, 2799, 3611, 2959, 1506, 436, 55 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,n) = Fibonacci(n+1) = A000045(n+1). A202390 is jointly generated with A208340 as an array of coefficients of polynomials v(n,x): initially, u(1,x)=v(1,x)=1; for n>1, u(n,x)=u(n-1,x)+x*v(n-1)x and v(n,x)=(x+1)*u(n-1,x)+(x+1)v(n-1,x).  The alternating row sums of A202390, and also A208340, are 0 except for the first one.  See the Mathematica section.  [From Clark Kimberling, Feb 27 2012] LINKS FORMULA T(n,k) = 2*T(n-1,k) + T(n-1,k-1) + T(n-2,k-2) - T(n-2,k) with T(0,0) = T(1,0) = T(1,1) = 1 and T(n,k) = 0 if k<0 or if n 1, {n, 1, z}]  (*row sums*) Table[u[n, x] /. x -> -1, {n, 1, z}] (*alt. row sums*) CROSSREFS Cf. A000012, A000217, A051744, A000045, A123585, A208340. Sequence in context: A139624 A132276 A257558 * A210858 A114586 A052174 Adjacent sequences:  A202387 A202388 A202389 * A202391 A202392 A202393 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Dec 18 2011 STATUS approved

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Last modified May 16 19:46 EDT 2021. Contains 343951 sequences. (Running on oeis4.)