A092966 Number of interior balls in a truncated tetrahedral arrangement.

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.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..2000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

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

Adjacent sequences: A092963 A092964 A092965 * A092967 A092968 A092969

Keyword

nonn,easy

Author

N. J. A. Sloane, May 08 2004

Status

approved