A259211 Positive octagonal numbers (A000567) that are other octagonal numbers divided by 3.
560, 4090071480, 29860802042948800, 218007803276760596488520, 1591631806178550455562538466640, 11620188673811755515268615201727379160, 84836696710140620657577957851546090689242080, 619375925014776443389412658082968133380998230391400
Offset: 1
Examples
560 is in the sequence because 560 is the 14th octagonal number, and 3*560=1680 is the 24th octagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..146
- Index entries for linear recurrences with constant coefficients, signature (7300803,-7300803,1).
Programs
-
Mathematica
CoefficientList[Series[40 (x^2 + 40545 x + 14)/((1 - x) (x^2 - 7300802 x + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 21 2015 *) LinearRecurrence[{7300803,-7300803,1},{560,4090071480,29860802042948800},20] (* Harvey P. Dale, Jan 28 2025 *) -
PARI
Vec(-40*x*(x^2+40545*x+14)/((x-1)*(x^2-7300802*x+1)) + O(x^20))
Formula
a(n) = 7300803*a(n-1)-7300803*a(n-2)+a(n-3).
G.f.: -40*x*(x^2+40545*x+14) / ((x-1)*(x^2-7300802*x+1)).