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

4, 9, 9, 16, 36, 16, 25, 100, 100, 25, 36, 225, 400, 225, 36, 49, 441, 1225, 1225, 441, 49, 64, 784, 3136, 4900, 3136, 784, 64, 81, 1296, 7056, 15876, 15876, 7056, 1296, 81, 100, 2025, 14400, 44100, 63504, 44100, 14400, 2025, 100, 121, 3025

Offset

2,1

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 2..5461

Tricia Muldoon Brown, The Problem of Pawns, arXiv:1811.09606 [math.CO], 2018.

Formula

a(n) = A014410(n)^2. - Sean A. Irvine, Nov 18 2018

Example

Triangle begins:
  4,
  9, 9,
  16, 36, 16,
  25, 100, 100, 25,
  36, 225, 400, 225, 36,
  ...

Maple

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

Mathematica

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

Crossrefs

Cf. A007318, A014410.

Sequence in context: A140978 A106410 A065737 * A139417 A329732 A298816

Adjacent sequences: A014716 A014717 A014718 * A014720 A014721 A014722

Keyword

nonn,tabl

Author

Mohammad K. Azarian

Extensions

More terms from Sean A. Irvine, Nov 18 2018

Offset corrected by Joerg Arndt, Nov 19 2018

Status

approved