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Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly five ways.
2

%I #14 Sep 08 2022 08:45:07

%S 17,165,678,1910,4335,8547,15260,25308,39645,59345,85602,119730,

%T 163163,217455,284280,365432,462825,578493,714590,873390,1057287,

%U 1268795,1510548,1785300,2095925,2445417,2836890,3273578,3758835,4296135,4889072,5541360

%N Sum of numbers that can be written as t*n + u*(n+1) for nonnegative integers t,u in exactly five ways.

%D Fred. Schuh, Vragen betreffende een onbepaalde vergelijking, Nieuw Tijdschrift voor Wiskunde, 52 (1964-1965) 193-198.

%H Vincenzo Librandi, <a href="/A076458/b076458.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n*(n+1)*(10*n^2+8*n-1)/2.

%F G.f.: x*(17+80*x+23*x^2)/(1-x)^5.

%p seq(1/2*n*(n+1)*(10*n^2+8*n-1),n=1..40);

%t CoefficientList[Series[(17 + 80 x + 23 x^2)/(1 - x)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 30 2013 *)

%o (Magma) [n*(n+1)*(10*n^2+8*n-1)/2: n in [1..50]]; // _Vincenzo Librandi_, Dec 30 2013

%Y Cf. A002417, A076454-A076459.

%K easy,nonn

%O 1,1

%A _Floor van Lamoen_, Oct 13 2002

%E More terms from _Vincenzo Librandi_, Dec 30 2013