

A285009


Subset sums (see Comments).


1



9, 17, 28, 42, 59, 79, 102, 128, 157, 189, 224, 262, 303, 347, 394, 444, 497, 553, 612, 674, 739, 807, 878, 952, 1029, 1109, 1192, 1278, 1367, 1459, 1554, 1652, 1753, 1857, 1964, 2074, 2187, 2303, 2422, 2544, 2669, 2797, 2928, 3062, 3199, 3339, 3482, 3628, 3777, 3929, 4084
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OFFSET

3,1


COMMENTS

For n > 2, take the set [3*(n1)] and form three subsets all of which: a) have cardinality of n, b) have the same sum of elements, and c) share one element with the other subset and another element with the third subset. a(n) is the sum of the elements of each subset.


REFERENCES

a(4) is mentioned in: Gary Gruber, "The World's 200 Hardest Brain Teasers", Sourcebooks, 2010, p. 55.


LINKS

Colin Barker, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 3*a(n1)  3*a(n2) + a(n3), for n > 5.
a(n) = (8 + (n2)*(3*n+1))/2, for n > 2.
G.f.: x^3*(9  10*x + 4*x^2) / (1  x)^3.  Colin Barker, Apr 08 2017
E.g.f.: (1/2)*exp(x)*(3*x^2  2*x + 6)  2*x*(x + 1)  3.  Indranil Ghosh, Apr 08 2017; corrected by Ilya Gutkovskiy, Apr 10 2017


EXAMPLE

For n = 3, the set is S = {1,2,3,4,5,6} and the subsets are S1 = {1,2,6}, S2 = {1,3,5} and S3 = {2,3,4}. Therefore, a(3) = 9.


MATHEMATICA

Table[(8+(n2)*(3 *n+1))/2, {n, 3, 53}]
Drop[CoefficientList[Series[x^3*(9  10*x + 4*x^2) / (1  x)^3 , {x, 0, 60}], x], 3] (* Indranil Ghosh, Apr 08 2017 *)


PROG

(PARI) Vec(x^3*(9  10*x + 4*x^2) / (1  x)^3 + O(x^60)) \\ Colin Barker, Apr 08 2017


CROSSREFS

Sequence in context: A235361 A109333 A081030 * A228260 A147459 A188559
Adjacent sequences: A285006 A285007 A285008 * A285010 A285011 A285012


KEYWORD

easy,nonn


AUTHOR

Ivan N. Ianakiev, Apr 07 2017


STATUS

approved



