OFFSET
0,3
COMMENTS
For 4 weights, 1, 3, 8, 23 works for values up to 28. For 5 weights, 10, 12, 13, 17, 51 works up to 56. The lowest set of n weights with f(n) distinct values is still unknown at this time.
Binomial transform of the sequence (0, 1, 2, 3, 3, 0, 0, 0, ....). - Paul Barry, Sep 05 2005
REFERENCES
Discovered by Tom Turrittin and Ed Pegg Jr.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Michal Opler, Pavel Valtr, and Tung Anh Vu, On the Arrangement of Hyperplanes Determined by n Points, EuroCG (39th European Workshop on Computational Geometry, Barcelona, Spain 2023) Session 7B, Talk 1, Vol. 54, No. 6.
Ed Pegg Jr., Commentary on weekly puzzles
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (n^4 - 2*n^3 + 7*n^2 + 2*n) / 8.
G.f.: -x*(x^3+2*x^2-x+1) / (x-1)^5. - Colin Barker, Apr 16 2013 [corrected by Georg Fischer, May 11 2019]
MATHEMATICA
CoefficientList[Series[- x (x^3 + 2 x^2 - x + 1)/(x - 1)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 21 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 4, 12, 31}, 50] (* Harvey P. Dale, Sep 03 2015 *)
PROG
(Magma) [(n^4-2*n^3+7*n^2+2*n)/8: n in [0..40]]; // Vincenzo Librandi, Oct 21 2013
(Python)
from __future__ import division
A037255_list = [n*(n*(n*(n - 2) + 7) + 2)//8 for n in range(10**3)] # Chai Wah Wu, Jan 22 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Oct 21 2013
STATUS
approved