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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
OFFSET
1,2
COMMENTS
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
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.
FORMULA
a(n) = (1/6)*(n-1)*(23*n^2-19*n+6).
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
G.f.: (10*x+12*x^2+x^3)/(x-1)^4. - Harvey P. Dale, Jun 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] (* Harvey P. Dale, Jun 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: A232909 A028994 A257042 * A281401 A050494 A367460
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 08 2004
STATUS
approved