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 A238731 Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)). 11
 1, 1, 1, 2, 4, 1, 5, 13, 7, 1, 13, 40, 33, 10, 1, 34, 120, 132, 62, 13, 1, 89, 354, 483, 308, 100, 16, 1, 233, 1031, 1671, 1345, 595, 147, 19, 1, 610, 2972, 5561, 5398, 3030, 1020, 203, 22, 1, 1597, 8495, 17984, 20410, 13893, 5943, 1610, 268, 25, 1, 4181 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Unsigned version of A124037 and A126126. Subtriangle of the triangle given by (0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Row sums are A001075(n). Diagonal sums are A133494(n). Sum_{k=0..n} T(n,k)*x^k = A001519(n), A001075(n), A002320(n), A038723(n), A033889(n) for x = 0, 1, 2, 3, 4 respectively. - Philippe Deléham, Mar 05 2014 LINKS FORMULA T(n,k) = 3*T(n-1,k) + T(n-1,k-1) - T(n-2,k), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. G.f.: (1-2*x)/(1-(y+3)*x+x^2). - Philippe Deléham, Mar 05 2014 EXAMPLE Triangle begins: 1; 1, 1; 2, 4, 1; 5, 13, 7, 1; 13, 40, 33, 10, 1; 34, 120, 132, 62, 13, 1; 89, 354, 483, 308, 100, 16, 1; 233, 1031, 1671, 1345, 595, 147, 19, 1;... Triangle (0, 1, 1, 1, 0, 0, 0, ...) DELTA (1, 0, 2, -2, 0, 0, ...) begins: 1; 0, 1; 0, 1, 1; 0, 2, 4, 1; 0, 5, 13, 7, 1; 0, 13, 40, 33, 10, 1; 0, 34, 120, 132, 62, 13, 1; 0, 89, 354, 483, 308, 100, 16, 1; 0, 233, 1031, 1671, 1345, 595, 147, 19, 1;... MATHEMATICA (* The function RiordanArray is defined in A256893. *) RiordanArray[(1-2#)/(1-3#+#^2)&, x/(1-3#+#^2)&, 10] // Flatten (* Jean-François Alcover, Jul 16 2019 *) CROSSREFS Cf. A001519, A000012, A016777, A062708. Cf. A001906, A124037, A126126. Sequence in context: A085059 A336164 A181336 * A124037 A126126 A090285 Adjacent sequences:  A238728 A238729 A238730 * A238732 A238733 A238734 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 03 2014 STATUS approved

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Last modified June 22 20:16 EDT 2021. Contains 345388 sequences. (Running on oeis4.)