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A090225 T(n,k) = Points in n-dimensional lattice of side length k with at least one coordinate = k and GCD of all coordinates = 1. 1
0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 7, 0, 0, 0, 4, 12, 15, 0, 0, 0, 4, 30, 50, 31, 0, 0, 0, 8, 42, 160, 180, 63, 0, 0, 0, 4, 84, 304, 750, 602, 127, 0, 0, 0, 12, 78, 656, 1890, 3304, 1932, 255, 0, 0, 0, 8, 162, 880, 4620, 10864, 14070, 6050, 511, 0, 0, 0, 12, 156, 1680, 8070 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Table of n, a(n) for n=0..71.

FORMULA

T(n, 0) = 0; T(n, k) = (k+1)^n - k^n - sum T(n, divisors of k)

EXAMPLE

T(3,2) = 12 because of the six permutations of (2,1,0) and three each of (2,1,1) and (2,2,1).

0;

0,  0;

0,  1,  0;

0,  0,  3,  0;

0,  0,  2,  7,  0;

0,  0,  4, 12, 15, 0;

0,  0,  4, 30, 50, 31,  0;

0,  0,  8, 42,160,180, 63, 0;

0,  0,  4, 84,304,750,602,127, 0;

0,  0, 12, 78,656,1890,3304,1932,255, 0;

MATHEMATICA

aux[n_, k_] := If[k == 0, 0, (k + 1)^n - k^n - Sum[aux[n, Divisors[k][[i]]], {i, 1, Length[Divisors[k]] - 1}]]

CROSSREFS

Cf. A090030.

Sequence in context: A081130 A174428 A308347 * A206705 A285014 A219551

Adjacent sequences:  A090222 A090223 A090224 * A090226 A090227 A090228

KEYWORD

nonn,tabl

AUTHOR

Joshua Zucker, Nov 24 2003

STATUS

approved

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Last modified September 20 18:29 EDT 2021. Contains 347588 sequences. (Running on oeis4.)