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 A182412 Triangle T(n,k), read by rows, given by (1, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 2, -1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. 0
 1, 1, 1, 3, 6, 3, 5, 17, 19, 7, 11, 48, 80, 60, 17, 21, 119, 270, 308, 177, 41, 43, 290, 823, 1256, 1087, 506, 99, 85, 677, 2321, 4447, 5147, 3601, 1411, 239, 171, 1556, 6234, 14360, 20806, 19424, 11416, 3864, 577 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Antidiagonal sums are in A077995. LINKS Table of n, a(n) for n=0..44. FORMULA G.f.: (1-y*x)/(1-(1+2*y)*x-(2+3*y+y^2)*x^2) T(n,k) = T(n-1,k) + 2*T(n-1,k-1) + 2*T(n-2,k) + 3*T(n-2,k-1) + T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = 1, T(2,0) = T(2,2) = 3, T(2,1) = 6 and T(n,k) = 0 if k<0 or if k>n. T(n,n) = A001333(n), T(n,0) = A001045(n+1). Sum_{k, 0<=k<=n} T(n,k)*(-1)^k = A000007(n). EXAMPLE Triangle begins 1 1, 1 3, 6, 3 5, 17, 19, 7 11, 48, 80, 60, 17 21, 119, 270, 308, 177, 41 43, 290, 823, 1256, 1087, 506, 99 85, 677, 2321, 4447, 5147, 3601, 1411, 239 CROSSREFS Cf. A001045, A001333, A077995, Sequence in context: A134548 A151865 A124860 * A038138 A010704 A338947 Adjacent sequences: A182409 A182410 A182411 * A182413 A182414 A182415 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Apr 27 2012 STATUS approved

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Last modified December 7 02:45 EST 2023. Contains 367622 sequences. (Running on oeis4.)