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A204462 Number of 2*n-element subsets that can be chosen from {1,2,...,12*n} having element sum n*(12*n+1). 1
1, 6, 318, 32134, 4083008, 587267282, 91403537276, 15027205920330, 2572042542065646, 454018964549333284, 82122490665668040962, 15150820045467016057500, 2841258381788564812646472, 540201085284535788002286246, 103917818379993516623446237348 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of partitions of n*(12*n+1) into 2*n distinct parts <=12*n.

LINKS

Table of n, a(n) for n=0..14.

EXAMPLE

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

MAPLE

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

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

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

    end:

a:= n-> b(n*(12*n+1), 12*n, 2*n):

seq(a(n), n=0..12);

MATHEMATICA

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

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

a[n_] := b[n(12n+1), 12n, 2n];

a /@ Range[0, 10] (* Jean-Fran├žois Alcover, Dec 07 2020, after Alois P. Heinz *)

CROSSREFS

Bisection of row n=6 of A204459.

Sequence in context: A074656 A233108 A207816 * A135397 A042421 A221884

Adjacent sequences:  A204459 A204460 A204461 * A204463 A204464 A204465

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 18 2012

STATUS

approved

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Last modified October 23 12:42 EDT 2021. Contains 348214 sequences. (Running on oeis4.)