A204464
Number of 2*n-element subsets that can be chosen from {1,2,...,16*n} having element sum n*(16*n+1).
Original entry on oeis.org
1, 8, 790, 148718, 35154340, 9408671330, 2725410001024, 834014033203632, 265724127467961324, 87318355216835049968, 29402690636348418710858, 10098693807141197229592054, 3525753285145412581617963136, 1248001014165722671454730108968, 446964111600452023289482445527716
Offset: 0
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}.
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b:= proc(n, i, t) option remember;
`if`(it*(2*i-t+1)/2, 0,
`if`(n=0, 1, b(n, i-1, t) +`if`(n b(n*(16*n+1), 16*n, 2*n):
seq(a(n), n=0..10);
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b[n_, i_, t_] /; it(2i-t+1)/2 = 0; b[0, , ] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[nJean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
A204465
Number of n-element subsets that can be chosen from {1,2,...,9*n} having element sum n*(9*n+1)/2.
Original entry on oeis.org
1, 1, 9, 85, 1143, 17053, 276373, 4721127, 83916031, 1537408202, 28851490163, 552095787772, 10736758952835, 211657839534446, 4221164530621965, 85031286025167082, 1727896040082882283, 35382865902724442331, 729502230296220422918, 15132164184348997874504
Offset: 0
a(2) = 9 because there are 9 2-element subsets that can be chosen from {1,2,...,18} having element sum 19: {1,18}, {2,17}, {3,16}, {4,15}, {5,14}, {6,13}, {7,12}, {8,11}, {9,10}.
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b:= proc(n, i, t) option remember;
`if`(it*(2*i-t+1)/2, 0,
`if`(n=0, 1, b(n, i-1, t) +`if`(n b(n*(9*n+1)/2, 9*n, n):
seq(a(n), n=0..20);
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b[n_, i_, t_] /; it(2i-t+1)/2 = 0; b[0, , ] = 1;
b[n_, i_, t_] := b[n, i, t] = b[n, i-1, t] + If[nJean-François Alcover, Dec 07 2020, after Alois P. Heinz *)
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