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A126562 Number of intersections of at least four edges in a cube of n X n X n smaller cubes. 0
0, 7, 32, 81, 160, 275, 432, 637, 896, 1215, 1600, 2057, 2592, 3211, 3920, 4725, 5632, 6647, 7776, 9025, 10400, 11907, 13552, 15341, 17280, 19375, 21632, 24057, 26656, 29435, 32400, 35557, 38912, 42471, 46240, 50225, 54432, 58867, 63536, 68445 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n-1) = n^3 -(12n-16): a(n-1) is the number of points in a cubic lattice of n^3 equally spaced points from which all the 12n-16 points on the 12 edges are removed. - Luciano Ancora, Jun 25 2015

LINKS

Table of n, a(n) for n=1..40.

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

FORMULA

a(n) = 6 * (n-1)^2 + (n-1)^3.

G.f.: x^2*(7+4*x-5*x^2)/(1-x)^4. - Colin Barker, Jul 29 2012

EXAMPLE

On a cube made of 3 X 3 X 3 smaller cubes, each of the 6 sides has 4 intersections of four edges and in the center, there are 8 intersections of six edges. 6 * 4 + 8 = 32, which is a(3).

MATHEMATICA

LinearRecurrence[{4, -6, 4, -1}, {0, 7, 32, 81}, 50] (* Vincenzo Librandi, Jun 27 2015 *)

PROG

(PARI) concat(0, Vec(x^2*(7+4*x-5*x^2)/(1-x)^4 + O(x^50))) \\ Michel Marcus, Jun 26 2015

(MAGMA) [6*(n-1)^2 + (n-1)^3: n in [1..40]]; // Vincenzo Librandi, Jun 27 2015

CROSSREFS

Sequence in context: A013650 A013656 A067982 * A190096 A254407 A219510

Adjacent sequences:  A126559 A126560 A126561 * A126563 A126564 A126565

KEYWORD

nonn,easy

AUTHOR

Jonathan R. Love (japanada11(AT)yahoo.ca), Mar 12 2007

STATUS

approved

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)