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%I #31 Sep 08 2022 08:45:13
%S 0,10,52,149,324,600,1000,1547,2264,3174,4300,5665,7292,9204,11424,
%T 13975,16880,20162,23844,27949,32500,37520,43032,49059,55624,62750,
%U 70460,78777,87724,97324,107600,118575,130272,142714,155924,169925,184740,200392,216904
%N Number of interior balls in a truncated tetrahedral arrangement.
%C For n > 0, A092966(n) is the number of 4-element subsets of {-n,...,0,...n} having sum n+1. - _Clark Kimberling_, Apr 05 2012
%D H. S. M. Coxeter, Polyhedral numbers, pp. 25-35 of R. S. Cohen, J. J. Stachel and M. W. Wartofsky, eds., For Dirk Struik: Scientific, historical and political essays in honor of Dirk J. Struik, Reidel, Dordrecht, 1974.
%H Vincenzo Librandi, <a href="/A092966/b092966.txt">Table of n, a(n) for n = 1..2000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = (1/6)*(n-1)*(23*n^2-19*n+6).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=10, a(2)=52, a(3)=149. - _Harvey P. Dale_, Jun 15 2011
%F G.f.: (10*x+12*x^2+x^3)/(x-1)^4. - _Harvey P. Dale_, Jun 15 2011
%t Table[(1/6)(n-1)(23*n^2-19n+6),{n,50}] (* or *) LinearRecurrence[ {4,-6,4,-1},{0,10,52,149},50] (* _Harvey P. Dale_, Jun 15 2011 *)
%o (PARI) a(n)=((23*n-42)*n+25)*n/6-1 \\ _Charles R Greathouse IV_, Jun 16 2011
%o (Magma) [(1/6)*(n-1)*(23*n^2-19*n+6): n in [1..40]]; // _Vincenzo Librandi_, Jun 16 2011
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, May 08 2004
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