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 A105728 Triangle read by rows: T(n,1) = 1, T(n,n) = n and for 1 < k < n: T(n,k) = T(n-1,k-1) + 2*T(n-1,k). 7
 1, 1, 2, 1, 5, 3, 1, 11, 11, 4, 1, 23, 33, 19, 5, 1, 47, 89, 71, 29, 6, 1, 95, 225, 231, 129, 41, 7, 1, 191, 545, 687, 489, 211, 55, 8, 1, 383, 1281, 1919, 1665, 911, 321, 71, 9, 1, 767, 2945, 5119, 5249, 3487, 1553, 463, 89, 10, 1, 1535, 6657, 13183, 15617, 12223, 6593, 2479, 641, 109, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Sum of n-th row = 3^(n-1): Sum_{k=1..n} T(n,k) = A000244(n-1); for n>1: T(n,2) = A083329(n-1), T(n,n-1) = A028387(n-2). LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened EXAMPLE Triangle begins as:   1;   1,  2;   1,  5,  3;   1, 11, 11,  4;   1, 23, 33, 19,  5;   1, 47, 89, 71, 29, 6; ... MAPLE T:= proc(n, k) option remember;       if k=1 then 1     elif k=n then n     else T(n-1, k-1) + 2*T(n-1, k)       fi     end: seq(seq(T(n, k), k=1..n), n=1..12); # G. C. Greubel, Nov 13 2019 MATHEMATICA T[n_, k_]:= T[n, k]= If[k==1, 1, If[k==n, n, T[n-1, k-1] + 2*T[n-1, k]]]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* G. C. Greubel, Nov 13 2019 *) PROG (Haskell) a105728 n k = a105728_tabl !! (n-1) !! (k-1) a105728_row n = a105728_tabl !! (n-1) a105728_tabl = iterate (\row -> zipWith (+) ([0] ++ tail row ++ [1]) \$                                 zipWith (+) ([0] ++ row) (row ++ [0])) [1] -- Reinhard Zumkeller, Jul 22 2013 (MAGMA) function T(n, k)   if k eq 1 then return 1;   elif k eq n then return n;   else return T(n-1, k-1) + 2*T(n-1, k);   end if;   return T; end function; [T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 13 2019 (Sage) @CachedFunction def T(n, k):     if (k==1): return 1     elif (k==n): return n     else: return T(n-1, k-1) + 2*T(n-1, k) [[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 13 2019 CROSSREFS Cf. A013609, A115068. Sequence in context: A209130 A330381 A210792 * A120095 A327631 A130197 Adjacent sequences:  A105725 A105726 A105727 * A105729 A105730 A105731 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Apr 18 2005 STATUS approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)