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 A119673 T(n, k) = 3*T(n-1, k-1) + T(n-1, k) for k < n and T(n, n) = 1, T(n, k) = 0, if k < 0 or k > n; triangle read by rows. 2
 1, 1, 1, 1, 4, 1, 1, 7, 13, 1, 1, 10, 34, 40, 1, 1, 13, 64, 142, 121, 1, 1, 16, 103, 334, 547, 364, 1, 1, 19, 151, 643, 1549, 2005, 1093, 1, 1, 22, 208, 1096, 3478, 6652, 7108, 3280, 1, 1, 25, 274, 1720, 6766, 17086, 27064, 24604, 9841, 1, 1, 28, 349, 2542, 11926, 37384, 78322, 105796, 83653, 29524, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n,k) = R(n,k,3) where R(n,k,m) = (1-m)^(-n+k)-m^(k+1)*Pochhammer(n-k, k+1)* hyper2F1([1,n+1],[k+2],m)/(k+1)!. - Peter Luschny, Jul 25 2014 EXAMPLE Triangle begins: 1; 1, 1; 1, 4, 1; 1, 7, 13, 1; 1, 10, 34, 40, 1; 1, 13, 64, 142, 121, 1; 1, 16, 103, 334, 547, 364, 1; 1, 19, 151, 643, 1549, 2005, 1093, 1; 1, 22, 208, 1096, 3478, 6652, 7108, 3280, 1; 1, 25, 274, 1720, 6766, 17086, 27064, 24604, 9841, 1; MAPLE T := (n, k, m) -> (1-m)^(-n+k)-m^(k+1)*pochhammer(n-k, k+1)* hypergeom([1, n+1], [k+2], m)/(k+1)!; A119673 := (n, k) -> T(n, k, 3); seq(print(seq(round(evalf(A119673(n, k))), k=0..n)), n=0..10); # Peter Luschny, Jul 25 2014 MATHEMATICA T[_, 0]=1; T[n_, n_]=1; T[n_, k_]/; 0n, 0, if(k==n, 1, 3*T(n-1, k-1) +T(n-1, k))); for(n=0, 12, for(k=0, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Nov 18 2019 (Magma) function T(n, k) if k lt 0 or k gt n then return 0; elif k eq n then return 1; else return 3*T(n-1, k-1) + T(n-1, k); end if; return T; end function; [T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 18 2019 (Sage) @CachedFunction def T(n, k): if (k<0 or k>n): return 0 elif (k==n): return 1 else: return 3*T(n-1, k-1) + T(n-1, k) [[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 18 2019 CROSSREFS Cf. A003462, A014915, A081271, A119258. Sequence in context: A209414 A193636 A232968 * A144447 A051455 A346875 Adjacent sequences: A119670 A119671 A119672 * A119674 A119675 A119676 KEYWORD easy,nonn,tabl AUTHOR Zerinvary Lajos, Jun 11 2006 EXTENSIONS Definition clarified by Philippe Deléham, Jun 13 2006 Entry revised by N. J. A. Sloane, Jun 19 2006 STATUS approved

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Last modified March 26 23:26 EDT 2023. Contains 361553 sequences. (Running on oeis4.)