A259162 -id:A259162 - cp's OEIS frontend

A259161 Positive pentagonal numbers (A000326) that are triangular numbers (A000217) divided by 2.

5, 48510, 465793515, 4472549283020, 42945417749765025, 412361896760694487530, 3959498889750770719498535, 38019107927025003687930446040, 365059470355795195660737423378045, 3505300996337237541709397051345542550, 33657899801770684519698434826282476187555

Offset: 1

Colin Barker, Jun 19 2015

			5 is in the sequence because 5 is the 2nd pentagonal number, and 2*5 is the 4th triangular number.

Colin Barker, Table of n, a(n) for n = 1..251
Index entries for linear recurrences with constant coefficients, signature (9603,-9603,1).

Cf. A000217, A000326, A074378, A259156-A259160, A259162-A259167.

LinearRecurrence[{9603, -9603, 1}, {5, 48510, 465793515}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-5*x*(99*x+1)/((x-1)*(x^2-9602*x+1)) + O(x^20))

G.f.: -5*x*(99*x+1) / ((x-1)*(x^2-9602*x+1)).

A259163 Positive heptagonal numbers (A000566) that are triangular numbers (A000217) divided by 2.

Original entry on oeis.org

18, 189, 37727235, 393298308, 78448579122960, 817809556618215, 163122994382238923193, 1700522115268371779430, 339191755844562643229618814, 3536001066647854270462804353, 705302447816298343956844397692383, 7352626249945315029422809413582264

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000566 and A074378 (even triangular numbers divided by 2). - Michel Marcus, Jun 20 2015

			18 is in the sequence because 18 is the 3rd heptagonal number, and 2*18 is the 8th triangular number.

Colin Barker, Table of n, a(n) for n = 1..317
Index entries for linear recurrences with constant coefficients, signature (1,2079362,-2079362,-1,1).

Cf. A000217, A000566, A074378, A259156-A259162, A259164-A259167.

LinearRecurrence[{1, 2079362, -2079362, -1, 1}, {18, 189, 37727235, 393298308, 78448579122960}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-9*x*(2*x^4+19*x^3+33170*x^2+19*x+2)/((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)) + O(x^20))

G.f.: -9*x*(2*x^4+19*x^3+33170*x^2+19*x+2) / ((x-1)*(x^2-1442*x+1)*(x^2+1442*x+1)).

cp's OEIS Frontend

A259161 Positive pentagonal numbers (A000326) that are triangular numbers (A000217) divided by 2.

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