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A037255 For n weights, number of combinations when limited to two weights per pan. 2
0, 1, 4, 12, 31, 70, 141, 259, 442, 711, 1090, 1606, 2289, 3172, 4291, 5685, 7396, 9469, 11952, 14896, 18355, 22386, 27049, 32407, 38526, 45475, 53326, 62154, 72037, 83056, 95295, 108841, 123784, 140217, 158236, 177940, 199431, 222814, 248197, 275691, 305410 (list; graph; refs; listen; history; text; internal format)
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

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

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

Cf. A038523.

Sequence in context: A074210 A299053 A005289 * A027658 A001982 A129707

Adjacent sequences:  A037252 A037253 A037254 * A037256 A037257 A037258

KEYWORD

easy,nonn

AUTHOR

Ed Pegg Jr

EXTENSIONS

More terms from Vincenzo Librandi, Oct 21 2013

STATUS

approved

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Last modified January 17 23:15 EST 2019. Contains 319251 sequences. (Running on oeis4.)