A259163 -id:A259163 - cp's OEIS frontend

A259162 Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) divided by 2.

6, 58311, 559902916, 5376187741821, 51622154137063026, 495675918647891434531, 4759480119234899417304336, 45700527609217585557064800441, 438816461344227137284036796530846, 4213515616126741362983735763224383551, 40458176507232509223142693514443734326556

Offset: 1

Colin Barker, Jun 19 2015

Intersection of A000384 and A193866 (even pentagonal numbers divided by 2). - Michel Marcus, Jun 20 2015

			6 is in the sequence because 6 is the 2nd hexagonal number, and 2*6 is the 3rd pentagonal 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. A000326, A000384, A193866, A259156-A259161, A259163-A259167.

LinearRecurrence[{9603, -9603, 1}, {6, 58311, 559902916}, 20] (* Vincenzo Librandi, Jun 20 2015 *)

Vec(-x*(x^2+693*x+6)/((x-1)*(x^2-9602*x+1)) + O(x^20))

G.f.: -x*(x^2+693*x+6) / ((x-1)*(x^2-9602*x+1)).

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

Original entry on oeis.org

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)).

cp's OEIS Frontend

A259162 Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) divided by 2.

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