A135051 Pyramid game person numbers that have integer solutions.

7, 79, 191, 407, 631, 991, 1327, 1831, 2279, 2927, 3487, 4279, 4951, 5887, 6671, 7751, 8647, 9871, 10879, 12247, 13367, 14879, 16111, 17767, 19111, 20911, 22367, 24311, 25879, 27967, 29647, 31879, 33671, 36047, 37951, 40471, 42487, 45151, 47279, 50087, 52327, 55279, 57631, 60727, 63191, 66431, 69007, 72391, 75079, 78607

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

Sequence in context: A140613 A139945 A023285 * A201860 A176130 A014232

Adjacent sequences: A135048 A135049 A135050 * A135052 A135053 A135054

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