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A092966
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Number of interior balls in a truncated tetrahedral arrangement.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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]
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REFERENCES
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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.
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LINKS
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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).
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FORMULA
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(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]
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A041186 A058827 A028994 * A050494 A200035 A119543
Adjacent sequences: A092963 A092964 A092965 * A092967 A092968 A092969
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane, May 08 2004
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STATUS
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approved
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