A259165 -id:A259165 - cp's OEIS frontend

A259164 Positive heptagonal numbers (A000566) that are squares (A000290) divided by 2.

18, 1877922, 194706720450, 20187582187830642, 2093088896203949915058, 217015642916030352905224578, 22500615886726770153715544792802, 2332908856150589340161504762302084050, 241880656000904788079898366611289133690962

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000566 and A001105 (even squares 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 6th square.

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, A001105, A259156-A259163, A259165-A259167.

LinearRecurrence[{103683, -103683, 1}, {18, 1877922, 194706720450}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-18*x*(x^2+646*x+1)/((x-1)*(x^2-103682*x+1)) + O(x^20))

G.f.: -18*x*(x^2+646*x+1) / ((x-1)*(x^2-103682*x+1)).

A259166 Positive heptagonal numbers (A000566) that are hexagonal numbers (A000384) divided by 2.

Original entry on oeis.org

189, 393298308, 817809556618215, 1700522115268371779430, 3536001066647854270462804353, 7352626249945315029422809413582264, 15288771624335254149144023973574781130123, 31790890742313650111822470662710981230881538170

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000566 and A033991 (even hexagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			189 is in the sequence because 189 is the 9th heptagonal number, and 2*189 is the 14th hexagonal number.

Colin Barker, Table of n, a(n) for n = 1..158
Index entries for linear recurrences with constant coefficients, signature (2079363,-2079363,1).

Cf. A000384, A000566, A259156-A259165, A259167.

I:=[189,393298308,817809556618215]; [n le 3 select I[n] else 2079363*Self(n-1)-2079363*Self(n-2)+Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 20 2015

LinearRecurrence[{2079363, -2079363, 1},{189, 393298308, 817809556618215}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-9*x*(2*x^2+33189*x+21)/((x-1)*(x^2-2079362*x+1)) + O(x^20))

G.f.: -9*x*(2*x^2+33189*x+21) / ((x-1)*(x^2-2079362*x+1)).

cp's OEIS Frontend

A259164 Positive heptagonal numbers (A000566) that are squares (A000290) divided by 2.

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