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%I #13 Sep 26 2016 21:29:56
%S 7,79,191,407,631,991,1327,1831,2279,2927,3487,4279,4951,5887,6671,
%T 7751,8647,9871,10879,12247,13367,14879,16111,17767,19111,20911,22367,
%U 24311,25879,27967,29647,31879,33671,36047,37951,40471,42487,45151,47279,50087,52327,55279,57631,60727,63191,66431,69007,72391,75079,78607
%N Pyramid game person numbers that have integer solutions.
%C This result comes from looking for "perfect Pyramids" which is equivalent to finding m values that satisfy m(m + 1)/2 + 1 - n == 0, for each n value.
%C Integer solutions have the form such that 2*sqrt( -7 + 8*n), is an integer, and Mod[n - 7, 8], are equivalent to zero, simultaneously.
%H G. C. Greubel, <a href="/A135051/b135051.txt">Table of n, a(n) for n = 1..468</a>
%F From _Colin Barker_, Apr 30 2012: (Start)
%F Conjecture: a(n) = 9 - 2*(-1)^n + 4*(-8+(-1)^n)*n + 32*n^2.
%F Conjecture: G.f.: x*(7 + 72*x + 98*x^2 + 72*x^3 + 7*x^4)/((1-x)^3*(1+x)^2). (End)
%t Flatten[Table[If[ IntegerQ[2*Sqrt[ -7 + 8*n]] && Mod[n - 7, 8] == 0, n, {}], {n, 1, 10000}]]
%K nonn,uned
%O 1,1
%A _Roger L. Bagula_, Jan 31 2008
%E a(19) to a(50) added and comments edited by _G. C. Greubel_, Sep 21 2016
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