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A014719 Squares of elements in Pascal triangle (by row) that are not 1. 1

%I #36 Dec 13 2018 12:44:07

%S 4,9,9,16,36,16,25,100,100,25,36,225,400,225,36,49,441,1225,1225,441,

%T 49,64,784,3136,4900,3136,784,64,81,1296,7056,15876,15876,7056,1296,

%U 81,100,2025,14400,44100,63504,44100,14400,2025,100,121,3025

%N Squares of elements in Pascal triangle (by row) that are not 1.

%C Number of ways to place 2k*(n-k) nonattacking ferses on a 2k X (2n-2k) board. - _Tricia Muldoon Brown_, Dec 12 2018

%H Vincenzo Librandi, <a href="/A014719/b014719.txt">Table of n, a(n) for n = 2..5461</a>

%H Tricia Muldoon Brown, <a href="https://arxiv.org/abs/1811.09606">The Problem of Pawns</a>, arXiv:1811.09606 [math.CO], 2018.

%F a(n) = A014410(n)^2. - _Sean A. Irvine_, Nov 18 2018

%e Triangle begins:

%e 4,

%e 9, 9,

%e 16, 36, 16,

%e 25, 100, 100, 25,

%e 36, 225, 400, 225, 36,

%e ...

%p T:=(n,k)->binomial(n,k)^2: seq(seq(T(n,k),k=1..n-1),n=2..11); # _Muniru A Asiru_, Dec 12 2018

%t Select[Flatten[Table[Binomial[n, i]^2, {n, 0, 25}, {i, 0, n}]], #>1 &] (* _Vincenzo Librandi_, Nov 19 2018 *)

%Y Cf. A007318, A014410.

%K nonn,tabl

%O 2,1

%A _Mohammad K. Azarian_

%E More terms from _Sean A. Irvine_, Nov 18 2018

%E Offset corrected by _Joerg Arndt_, Nov 19 2018

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Last modified April 24 10:11 EDT 2024. Contains 371935 sequences. (Running on oeis4.)