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A204469 Number of 5-element subsets that can be chosen from {1,2,...,10*n+5} having element sum 25*n+15. 2

%I #15 Oct 31 2018 17:03:57

%S 1,141,1394,5910,17053,39361,78602,141702,236833,373309,561704,813722,

%T 1142341,1561651,2087034,2734970,3523243,4470721,5597592,6925112,

%U 8475873,10273519,12343044,14710482,17403231,20449711,23879724,27724080,32014983,36785631,42070632

%N Number of 5-element subsets that can be chosen from {1,2,...,10*n+5} having element sum 25*n+15.

%C a(n) is the number of partitions of 25*n+15 into 5 distinct parts <= 10*n+5.

%H Alois P. Heinz, <a href="/A204469/b204469.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: -(12*x^10 +390*x^9 +1821*x^8 +4057*x^7 +6070*x^6 +6651*x^5 +5374*x^4 +3123*x^3 +1112*x^2 +139*x+1) / ((x^2+x+1)*(x^2+1)*(x+1)^2*(x-1)^5).

%e a(0) = 1 because there is 1 5-element subset that can be chosen from {1,2,3,4,5} having element sum 15: {1,2,3,4,5}.

%p a:= n-> (Matrix(11, (i, j)-> `if`(i=j-1, 1, `if`(i=11, [1, -2, 0, 1, 0, 2, -2, 0, -1, 0, 2][j], 0)))^n. <<1, 141, 1394, 5910, 17053, 39361, 78602, 141702, 236833, 373309, 561704>>)[1, 1]: seq(a(n), n=0..50);

%Y Bisection of column k=5 of A204459.

%K nonn,easy

%O 0,2

%A _Alois P. Heinz_, Jan 16 2012

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Last modified March 1 19:16 EST 2024. Contains 370443 sequences. (Running on oeis4.)