A259160 -id:A259160 - cp's OEIS frontend

A259159 Positive squares (A000290) that are heptagonal numbers (A000566) divided by 2.

9, 938961, 97353360225, 10093791093915321, 1046544448101974957529, 108507821458015176452612289, 11250307943363385076857772396401, 1166454428075294670080752381151042025, 120940328000452394039949183305644566845481

Offset: 1

Colin Barker, Jun 19 2015

			9 is in the sequence because 9 is the 3rd square, and 2*9 is the 3rd heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (103683,-103683,1).

Cf. A000290, A000566, A259156-A259158, A259160-A259167.

LinearRecurrence[{103683, -103683, 1},{9, 938961, 97353360225}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-9*x*(x^2+646*x+1)/((x-1)*(x^2-103682*x+1)) + O(x^20))

G.f.: -9*x*(x^2+646*x+1) / ((x-1)*(x^2-103682*x+1)).

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

Original entry on oeis.org

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)).

cp's OEIS Frontend

A259159 Positive squares (A000290) that are heptagonal numbers (A000566) divided by 2.

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