A131215 -id:A131215 - cp's OEIS frontend

A280071 Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).

1, 12, 232, 4621, 92181, 1838992, 36687652, 731914041, 14601593161, 291299949172, 5811397390272, 115936647856261, 2312921559734941, 46142494546842552, 920536969377116092, 18364596892995479281, 366371400890532469521, 7309063420917653911132

Offset: 1

Colin Barker, Dec 25 2016

Also positive integers x in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of y being A280072.

			12 is in the sequence because the 12th 11-gonal number is 606, which is also the 11th centered 11-gonal number.

Colin Barker, Table of n, a(n) for n = 1..750
Index entries for linear recurrences with constant coefficients, signature (21,-21,1).

Cf. A051682, A060544, A131215, A280072

LinearRecurrence[{21,-21,1},{1,12,232},20] (* Harvey P. Dale, May 27 2025 *)

Vec(x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30))

a(n) = (14 + (11-3*sqrt(11))*(10+3*sqrt(11))^n + (10+3*sqrt(11))^(-n)*(11+3*sqrt(11)))/36.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)).

A280072 Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682).

Original entry on oeis.org

1, 11, 210, 4180, 83381, 1663431, 33185230, 662041160, 13207637961, 263490718051, 5256606723050, 104868643742940, 2092116268135741, 41737456718971871, 832657018111301670, 16611402905507061520, 331395401092029928721, 6611296618935091512891

Offset: 1

Colin Barker, Dec 25 2016

Also positive integers y in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of x being A280071.

			11 is in the sequence because the 11th centered 11-gonal number is 606, which is also the 12th 11-gonal number.

Colin Barker, Table of n, a(n) for n = 1..750
Index entries for linear recurrences with constant coefficients, signature (21,-21,1).

Cf. A051682, A060544, A131215, A280071.

LinearRecurrence[{21,-21,1},{1,11,210},20] (* Harvey P. Dale, Aug 19 2020 *)

Vec(x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30)) \\ Colin Barker, Dec 25 2016

a(n) = (6 - (3+sqrt(11))*(10+3*sqrt(11))^(-n) + (-3+sqrt(11))*(10+3*sqrt(11))^n)/12.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)).

cp's OEIS Frontend

A280071 Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).

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