A204464 - OEIS

%I #11 Dec 07 2020 02:08:05

%S 1,8,790,148718,35154340,9408671330,2725410001024,834014033203632,

%T 265724127467961324,87318355216835049968,29402690636348418710858,

%U 10098693807141197229592054,3525753285145412581617963136,1248001014165722671454730108968,446964111600452023289482445527716

%N Number of 2*n-element subsets that can be chosen from {1,2,...,16*n} having element sum n*(16*n+1).

%C a(n) is the number of partitions of n*(16*n+1) into 2*n distinct parts <=16*n.

%e a(1) = 8 because there are 8 2-element subsets that can be chosen from {1,2,...,16} having element sum 17: {1,16}, {2,15}, {3,14}, {4,13}, {5,12}, {6,11}, {7,10}, {8,9}.

%p b:= proc(n, i, t) option remember;

%p       `if`(i<t or n<t*(t+1)/2 or n>t*(2*i-t+1)/2, 0,

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

%p     end:

%p a:= n-> b(n*(16*n+1), 16*n, 2*n):

%p seq(a(n), n=0..10);

%t b[n_, i_, t_] /; i<t || n<t(t+1)/2 || n>t(2i-t+1)/2 = 0; b[0, _, _] = 1;

%t b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[n<i, 0, b[n-i, i-1, t-1]];

%t a[n_] := b[n(16n+1), 16n, 2n];

%t a /@ Range[0, 10] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)

%Y Bisection of row n=8 of A204459.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jan 18 2012