OFFSET
1,1
COMMENTS
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.
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..468
FORMULA
From Colin Barker, Apr 30 2012: (Start)
Conjecture: a(n) = 9 - 2*(-1)^n + 4*(-8+(-1)^n)*n + 32*n^2.
Conjecture: G.f.: x*(7 + 72*x + 98*x^2 + 72*x^3 + 7*x^4)/((1-x)^3*(1+x)^2). (End)
MATHEMATICA
Flatten[Table[If[ IntegerQ[2*Sqrt[ -7 + 8*n]] && Mod[n - 7, 8] == 0, n, {}], {n, 1, 10000}]]
CROSSREFS
KEYWORD
nonn,uned
AUTHOR
Roger L. Bagula, Jan 31 2008
EXTENSIONS
a(19) to a(50) added and comments edited by G. C. Greubel, Sep 21 2016
STATUS
approved