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 A179441 Number of solutions to a+b+c < d+e with each of a,b,c,d,e in {1..n+1}. 1
 1, 21, 121, 432, 1182, 2723, 5558, 10368, 18039, 29689, 46695, 70720, 103740, 148071, 206396, 281792, 377757, 498237, 647653, 830928, 1053514, 1321419, 1641234, 2020160, 2466035, 2987361, 3593331, 4293856, 5099592, 6021967, 7073208, 8266368, 9615353, 11134949, 12840849 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A197083. Sequence in context: A044734 A325484 A200888 * A164785 A179956 A117388 Adjacent sequences:  A179438 A179439 A179440 * A179442 A179443 A179444 KEYWORD nonn AUTHOR Bobby Milazzo, Jul 14 2010 EXTENSIONS Name edited and terms a(24) and beyond from Andrew Howroyd, Apr 15 2021 STATUS approved

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Last modified July 28 15:51 EDT 2021. Contains 346335 sequences. (Running on oeis4.)