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A051666 Rows of triangle formed using Pascal's rule except begin and end n-th row with n^2. 6

%I

%S 0,1,1,4,2,4,9,6,6,9,16,15,12,15,16,25,31,27,27,31,25,36,56,58,54,58,

%T 56,36,49,92,114,112,112,114,92,49,64,141,206,226,224,226,206,141,64,

%U 81,205,347,432,450,450,432,347,205,81,100,286,552,779,882,900,882,779

%N Rows of triangle formed using Pascal's rule except begin and end n-th row with n^2.

%C Row sums give 6*2^n - 4*n - 6 (A051667).

%C Central terms: T(2*n,n) = 2 * A220101(n). - _Reinhard Zumkeller_, Aug 05 2013

%C For a closed-form formula for arbitrary left and right borders of Pascal like triangle see A228196. - _Boris Putievskiy_, Aug 19 2013

%C For a closed-form formula for generalized Pascal's triangle see A228576. - _Boris Putievskiy_, Sep 09 2013

%H Reinhard Zumkeller, <a href="/A051666/b051666.txt">Rows n = 0..100 of table, flattened</a>

%e Triangle begins:

%e 0;

%e 1, 1;

%e 4, 2, 4;

%e 9, 6, 6, 9;

%e 16, 15, 12, 15, 16;

%e ...

%t T[n_, 0] := n^2; T[n_, n_] := n^2;

%t T[n_, k_] := T[n, k] = T[n-1, k-1] + T[n-1, k];

%t Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-Fran├žois Alcover_, Jul 13 2018 *)

%o (Haskell)

%o a051666 n k = a051666_tabl !! n !! k

%o a051666_row n = a051666_tabl !! n

%o a051666_tabl = map fst $ iterate

%o (\(vs, w:ws) -> (zipWith (+) ([w] ++ vs) (vs ++ [w]), ws))

%o ([0], [1, 3 ..])

%o -- _Reinhard Zumkeller_, Aug 05 2013

%Y Cf. A007318, A000290, A005408, A228196, A228576.

%K easy,nonn,tabl

%O 0,4

%A Asher Auel (asher.auel(AT)reed.edu)

%E More terms from _James A. Sellers_

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Last modified April 4 21:43 EDT 2020. Contains 333238 sequences. (Running on oeis4.)