A106175 Numbers n such that n^2 = 67*m^2 + 67*m + 1.

1, 135, 11791, 3186521, 278253009, 14755412411, 24297576265, 1288470373299, 112511657189035, 30406305506223725, 2655135804746536821, 140798562959107191995, 231851453975691325309, 12294795423043604534211, 1073604668382849022129099, 290141949335169200729049629

Offset

1,2

Links

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,9542163854,0,0,0,0,0,-1).

Formula

a(1)=1, a(2)=135, a(3)=11791, a(4)=3186521, a(5)=278253009, a(6)=14755412411, a(7)=9542163854*a(1)+a(6), a(8)=9542163854*a(2)+a(5), a(9)=9542163854*a(3)+a(4), a(10)=9542163854*a(4)+a(3), a(11)=9542163854*a(5)+a(2), a(12)=9542163854*a(6)+a(1), then a(n)=9542163854*a(n-6)-a(n-12).

G.f.: x*(x^11 +135*x^10 +11791*x^9 +3186521*x^8 +278253009*x^7 +14755412411*x^6 +14755412411*x^5 +278253009*x^4 +3186521*x^3 +11791*x^2 +135*x +1) / ((x^6 -97684*x^3 +1)*(x^6 +97684*x^3 +1)). [Colin Barker, Mar 07 2013]

Crossrefs

Cf. A106176 (associated m).

Sequence in context: A076011 A132054 A273440 * A203625 A051307 A056740

Adjacent sequences: A106172 A106173 A106174 * A106176 A106177 A106178

Keyword

nonn,easy

Author

Pierre CAMI, Apr 24 2005

Extensions

a(15)-a(16) from Colin Barker, Mar 07 2013

Status

approved