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A182260 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w<x+y. 8

%I #14 Aug 10 2019 14:47:15

%S 0,3,11,28,56,99,159,240,344,475,635,828,1056,1323,1631,1984,2384,

%T 2835,3339,3900,4520,5203,5951,6768,7656,8619,9659,10780,11984,13275,

%U 14655,16128,17696,19363,21131,23004,24984,27075,29279,31600,34040

%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w<x+y.

%C Also the number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w>x+y.

%C A182260(n)+A055232(n)=3^(n-1).

%C A182260 is row 1 of A211802 and also row 1 of A182259; see A211790 for a discussion and guide to related sequences.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).

%F a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

%F a(n) = (-1+(-1)^n-2*n^2+4*n^3)/8. G.f.: x^2*(3+2*x+x^2)/((1-x)^4*(1+x)). [_Colin Barker_, May 06 2012]

%e For n=2, the 3 triples (w,x,y) for which 2w<x+y are (1,1,2), (1,2,1), (1,2,2). The 3 triples for which 2w>x+y are (2,1,1), (2,1,2), (2,2,1).

%t (See the program at A211802.)

%t LinearRecurrence[{3,-2,-2,3,-1},{0,3,11,28,56},50] (* _Harvey P. Dale_, Aug 10 2019 *)

%Y Cf. A211790, A211802.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Apr 22 2012

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Last modified March 29 03:41 EDT 2024. Contains 371264 sequences. (Running on oeis4.)