A121338 -id:A121338 - cp's OEIS frontend

A259210 Positive hexagonal numbers (A000384) that are other hexagonal numbers divided by 3.

15, 567645, 21362755051, 803965923024825, 30256453525753512135, 1138671371184241752666901, 42852758352891300594112643235, 1612720706714039835374593462842225, 60693131033623416811596149786491655551, 2284125291706662961573569665690233502167245

Offset: 1

Colin Barker, Jun 21 2015

			15 is in the sequence because 15 is the 3rd hexagonal number, and 3*15 is the 5th hexagonal number.

Colin Barker, Table of n, a(n) for n = 1..219
Index entries for linear recurrences with constant coefficients, signature (37635,-37635,1).

Cf. A000384, A076139, A121338, A259211.

Vec(-x*(x^2+3120*x+15)/((x-1)*(x^2-37634*x+1)) + O(x^20))

a(n) = 37635*a(n-1)-37635*a(n-2)+a(n-3).

G.f.: -x*(x^2+3120*x+15) / ((x-1)*(x^2-37634*x+1)).

A259211 Positive octagonal numbers (A000567) that are other octagonal numbers divided by 3.

Original entry on oeis.org

560, 4090071480, 29860802042948800, 218007803276760596488520, 1591631806178550455562538466640, 11620188673811755515268615201727379160, 84836696710140620657577957851546090689242080, 619375925014776443389412658082968133380998230391400

Offset: 1

Colin Barker, Jun 21 2015

			560 is in the sequence because 560 is the 14th octagonal number, and 3*560=1680 is the 24th octagonal number.

Colin Barker, Table of n, a(n) for n = 1..146
Index entries for linear recurrences with constant coefficients, signature (7300803,-7300803,1).

Cf. A000567, A076139, A121338, A259210.

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 *)

Vec(-40*x*(x^2+40545*x+14)/((x-1)*(x^2-7300802*x+1)) + O(x^20))

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)).

cp's OEIS Frontend

A259210 Positive hexagonal numbers (A000384) that are other hexagonal numbers divided by 3.

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