

A204468


Number of 4element subsets that can be chosen from {1,2,...,4*n} having element sum 8*n+2.


2



0, 1, 8, 33, 86, 177, 318, 519, 790, 1143, 1588, 2135, 2796, 3581, 4500, 5565, 6786, 8173, 9738, 11491, 13442, 15603, 17984, 20595, 23448, 26553, 29920, 33561, 37486, 41705, 46230, 51071, 56238, 61743, 67596, 73807, 80388, 87349, 94700, 102453, 110618, 119205
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OFFSET

0,3


COMMENTS

a(n) is the number of partitions of 8*n+2 into 4 distinct parts <= 4*n.


LINKS



FORMULA

G.f.: x*(5*x^4+9*x^3+12*x^2+5*x+1)/((x^2+x+1)*(x1)^4).


EXAMPLE

a(2) = 8 because there are 8 4element subsets that can be chosen from {1,2,...,8} having element sum 18: {1,2,7,8}, {1,3,6,8}, {1,4,5,8}, {1,4,6,7}, {2,3,5,8}, {2,3,6,7}, {2,4,5,7}, {3,4,5,6}.


MAPLE

a:= n> ((9+(16*n18)*n)*n +[0, 2, 2][irem(n, 3)+1])/9:
seq(a(n), n=0..50);


MATHEMATICA

LinearRecurrence[{3, 3, 2, 3, 3, 1}, {0, 1, 8, 33, 86, 177}, 50] (* or *) CoefficientList[Series[(x (1+5 x+12 x^2+9 x^3+5 x^4))/((1+x)^4 (1+x+x^2)), {x, 0, 50}], x] (* Harvey P. Dale, Feb 25 2021 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



