Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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