A172244 Integers (up to a sign) that are not representable in the form 2x^2 + xy + 3y^2 + z^3 - z for integer x,y,z.

1, 599, 14951, 9314449, 232488049, 144839681351, 3615189146999, 2252257035693601, 56216191003346401, 35022596760195814199, 874161766486847388551, 544601377368787875100849, 13593215412654285888621649, 8468551383062054697622387751, 211374498792612379081219253399, 131685973462013573179240254427201

Offset

1,2

Comments

Odd positive integers C such that 27*C^2 - 4 = 23*D^2, where D is integer.

Links

Colin Barker, Table of n, a(n) for n = 1..450

William C. Jagy, following Irving Kaplansky, 2009. Integers not represented by 2x^2 + xy + 3y^2 + z^3 - z

William C. Jagy, Integers not represented by x^2 + xy + 3y^2 + z^3 - z, MathOverflow.

Index entries for linear recurrences with constant coefficients, signature (0,15550,0,-1).

Formula

For n>4, a(n) = 15550*a(n-2) - a(n-4).

G.f.: x*(1 - x)*(1 + 600*x + x^2) / (1 - 15550*x^2 + x^4). - Colin Barker, Mar 31 2018

Prog

(PARI) Vec(x*(1 - x)*(1 + 600*x + x^2) / (1 - 15550*x^2 + x^4) + O(x^20)) \\ Colin Barker, Mar 31 2018

Crossrefs

Sequence in context: A250937 A261701 A362324 * A090222 A361900 A216058

Adjacent sequences: A172241 A172242 A172243 * A172245 A172246 A172247

Keyword

nonn,easy

Author

Artur Jasinski, Jan 29 2010

Extensions

More terms from Max Alekseyev, Dec 15 2013

Status

approved