A238640 - OEIS

%I #29 Feb 20 2020 20:30:30

%S 1,1,3,19,168,1582,15546,157051,1625368,17159223,184277224,2008388660,

%T 22172275440,247558926150,2791793968821,31764451979736,

%U 364283594455091,4207485803818522,48908343969469479,571811846280602486,6720473048598172508,79363083519870386700

%N Position of [n, n, ..., n] (n n's) in Mathematica-ordered list of partitions of n^2.

%H Alois P. Heinz, <a href="/A238640/b238640.txt">Table of n, a(n) for n = 0..140</a>

%e The partitions of 4 in Mathematica order are 4, 31, 22, 211, 1111.  The position of 22 is a(2) = 3.

%p b:= proc(n, i) option remember; `if`(n=0, 1,

%p       `if`(i<1, 0, b(n, i-1) +`if`(i>n, 0, b(n-i, i))))

%p     end:

%p a:= n-> 1 +add(b(n^2-j, j), j=n+1..n^2):

%p seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 03 2014

%t r[n_] := Table[n, {k, 1, n}]; Flatten[Table[Position[IntegerPartitions[n^2], r[n]], {n, 0, 8}]]

%t b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, b[n, i-1]+If[i>n, 0, b[n-i, i]]]]; a[n_] := 1+Sum[b[n^2-j, j], {j, n+1, n^2}]; Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Oct 28 2015, after _Alois P. Heinz_ *)

%Y Cf. A000290, A072213, A080577 (Mathematica ordering), A238638, A238639, A330661, A332706.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 04 2014

%E a(9)-a(21) from _Alois P. Heinz_, Sep 03 2014