OFFSET
1,2
REFERENCES
Mathematics and Computer Education 1988 - 89 #261 Unsolved.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = (1/120)*(27*n^5 + 80*n^4 + 65*n^3 - 20*n^2 - 32*n).
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 6.
G.f.: x*(1 + 15*x + 10*x^2 + x^3)/(1 - x)^6.
EXAMPLE
a(1) = 1 since from {1,2} there is only one solution: {1,1,1} for a,b,c and {2,2} for d,e.
a(2) = 21 since from {1,2,3} there are 21 ways to select a,b,c,d,e such that a+b+c < d+e.
MATHEMATICA
k=10;
Table[p=Expand[Sum[x^k, {k, 1, n}]^2 Sum[1/x^k, {k, 1, n}]^3];
Twowins=Drop[CoefficientList[p, x], 1]//Total, {n, 2, k}]
PROG
(PARI) a(n)=(27*n^5 + 80*n^4 + 65*n^3 - 20*n^2 - 32*n)/120 \\ Andrew Howroyd, Apr 15 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bobby Milazzo, Jul 14 2010
EXTENSIONS
Name edited and terms a(24) and beyond from Andrew Howroyd, Apr 15 2021
STATUS
approved