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 A125166 Triangle, companion to A125165, left border = n^3. 0

%I

%S 1,8,1,27,9,1,64,36,10,1,125,100,46,11,1,216,225,146,57,12,1,343,441,

%T 371,203,69,13,1,512,784,812,574,272,82,14,1,729,1296,1596,1386,846,

%U 354,96,15,1

%N Triangle, companion to A125165, left border = n^3.

%C Column next to left border = (1, 9, 36, 100, 225...) squares of triangular numbers. A125165 uses analogous operations with n^2 on the left border instead of n^3. Row sums = 1, 9, 37, 111, 283, 657...a sequence analogous to row sums for A125165; i.e. A050488: (1, 5, 15, 37, 83, 177...).

%C Riordan array ((1+4*x+x^2)/(1-x)^4, x/(1-x)). - _Philippe DelĂ©ham_, Dec 09 2013

%F Binomial transform of an infinite matrix M with diagonal D, subdiagonal (D-1)..., etc; as follows: (D) = (1,1,1...); (D-1) = (7,7,7...); (D-2) = (12,12,12...); (D-3) = (6,6,6...). Alternatively, given left border n^3: (1, 8, 27, 64...); for k>1, T(n,k) = (n-1,k) + (n-1,k-1).

%e (5,3) = 146 = (4,3) + (4,2) = 46 + 100.

%e First few rows of the triangle are:

%e 1;

%e 8, 1;

%e 27, 9, 1;

%e 64, 36, 10, 1;

%e 125, 100, 46, 11, 1;

%e 216, 225, 146, 57, 12, 1;

%e 343, 441, 371, 203, 69, 13, 1;

%e 512, 784, 812, 574, 272, 82, 14, 1;

%e ...

%Y Cf. A000578, A125165, A050488.

%K nonn,tabl,changed

%O 0,2

%A _Gary W. Adamson_, Nov 22 2006

%E a(27) corrected by _Georg Fischer_, Feb 18 2020

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)