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 A092966 Number of interior balls in a truncated tetrahedral arrangement. 1
 0, 10, 52, 149, 324, 600, 1000, 1547, 2264, 3174, 4300, 5665, 7292, 9204, 11424, 13975, 16880, 20162, 23844, 27949, 32500, 37520, 43032, 49059, 55624, 62750, 70460, 78777, 87724, 97324, 107600, 118575, 130272, 142714, 155924, 169925, 184740, 200392, 216904 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For n>0, A092966(n) is the number 4-element subsets of {-n,...,0,...n} having sum n+1. [From Clark Kimberling, Apr 05 2012] REFERENCES 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..2000 Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA (1/6)*(n-1)*(23*n^2-19*n+6). a(0)=0, a(1)=10, a(2)=52, a(3)=149, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4) [From Harvey P. Dale, June 15 2011] G.f.: (10*x+12*x^2+x^3)/(x-1)^4 [From Harvey P. Dale, June 15 2011] MATHEMATICA Table[(1/6)(n-1)(23*n^2-19n+6), {n, 50}] (* or *) LinearRecurrence[ {4, -6, 4, -1}, {0, 10, 52, 149}, 50] (* From Harvey P. Dale, June 15 2011 *) PROG (PARI) a(n)=((23*n-42)*n+25)*n/6-1 \\ Charles R Greathouse IV, Jun 16 2011 (MAGMA) [(1/6)*(n-1)*(23*n^2-19*n+6): n in [1..40]]; // Vincenzo Librandi, Jun 16 2011 CROSSREFS Sequence in context: A041186 A058827 A028994 * A050494 A200035 A119543 Adjacent sequences:  A092963 A092964 A092965 * A092967 A092968 A092969 KEYWORD nonn,easy,changed AUTHOR N. J. A. Sloane, May 08 2004 STATUS approved

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