A051666 - OEIS

%I #25 Oct 27 2023 22:00:44

%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-François 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_

%E More terms from _James A. Sellers_