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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 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 A200035

Adjacent sequences:  A092963 A092964 A092965 * A092967 A092968 A092969

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 08 2004

STATUS

approved

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Last modified June 13 00:04 EDT 2021. Contains 344980 sequences. (Running on oeis4.)