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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.)