A254855 -id:A254855 - cp's OEIS frontend

A254856 Indices of centered heptagonal numbers (A069099) that are also octagonal numbers (A000567).

1, 2, 15, 40, 377, 1026, 9775, 26624, 253761, 691186, 6587999, 17944200, 171034201, 465858002, 4440301215, 12094363840, 115276797377, 313987601826, 2992756430575, 8151583283624, 77696390397561, 211627177772386, 2017113393905999, 5494155038798400

Offset: 1

Colin Barker, Feb 08 2015

Also positive integers y in the solutions to 6*x^2 - 7*y^2 - 4*x + 7*y - 2 = 0, the corresponding values of x being A254855.

			15 is in the sequence because the 15th centered heptagonal number is 736, which is also the 16th octagonal number.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,26,-26,-1,1).

Cf. A000567, A069099, A254855, A254857.

LinearRecurrence[{1,26,-26,-1,1},{1,2,15,40,377},30] (* Harvey P. Dale, Apr 30 2019 *)

Vec(x*(x^3+13*x^2-x-1)/((x-1)*(x^4-26*x^2+1)) + O(x^100))

a(n) = a(n-1)+26*a(n-2)-26*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(x^3+13*x^2-x-1) / ((x-1)*(x^4-26*x^2+1)).

A254857 Octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).

Original entry on oeis.org

1, 8, 736, 5461, 496133, 3680776, 334392976, 2480837633, 225380369761, 1672080883936, 151906034826008, 1126980034935301, 102384442092359701, 759582871465509008, 69006962064215612536, 511957728387718136161, 46510590046839230489633, 345058749350450558263576

Offset: 1

Colin Barker, Feb 08 2015

			736 is in the sequence because it is the 16th octagonal number and the 15th centered heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..708
Index entries for linear recurrences with constant coefficients, signature (1,674,-674,-1,1).

Cf. A000567, A069099, A254855, A254856.

Vec(-x*(x^4+7*x^3+54*x^2+7*x+1)/((x-1)*(x^2-26*x+1)*(x^2+26*x+1)) + O(x^100))

a(n) = a(n-1)+674*a(n-2)-674*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+7*x^3+54*x^2+7*x+1) / ((x-1)*(x^2-26*x+1)*(x^2+26*x+1)).

cp's OEIS Frontend

A254856 Indices of centered heptagonal numbers (A069099) that are also octagonal numbers (A000567).

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