A253675 -id:A253675 - cp's OEIS frontend

A253673 Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).

1, 16, 65, 1520, 6321, 148896, 619345, 14590240, 60689441, 1429694576, 5946945825, 140095478160, 582740001361, 13727927165056, 57102573187505, 1345196766697280, 5595469432374081, 131815555209168336, 548298901799472385, 12916579213731799600

Offset: 1

Colin Barker, Jan 08 2015

Also positive integers x in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of y being A253674.

Also indices of centered square numbers (A001844) that are also octagonal numbers (A000567). - Colin Barker, Feb 10 2015

			16 is in the sequence because the 16th centered triangular number is 361, which is also the 10th centered octagonal number.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Cf. A005448, A016754, A253674, A253675.

Cf. A000567, A001844, A254895, A254896.

LinearRecurrence[{1,98,-98,-1,1},{1,16,65,1520,6321},20] (* Harvey P. Dale, Aug 07 2023 *)

Vec(x*(3*x-1)*(5*x^2+18*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(3*x-1)*(5*x^2+18*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

A253674 Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448).

Original entry on oeis.org

1, 10, 40, 931, 3871, 91180, 379270, 8934661, 37164541, 875505550, 3641745700, 85790609191, 356853914011, 8406604195120, 34968041827330, 823761420512521, 3426511245164281, 80720212606031890, 335763133984272160, 7909757073970612651, 32901360619213507351

Offset: 1

Colin Barker, Jan 08 2015

Also positive integers y in the solutions to 3*x^2 - 8*y^2 - 3*x + 8*y = 0, the corresponding values of x being A253673.

			10 is in the sequence because the 10th centered octagonal number is 361, which is also the 16th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,98,-98,-1,1).

Cf. A005448, A016754, A253673, A253675.

LinearRecurrence[{1,98,-98,-1,1},{1,10,40,931,3871},30] (* Harvey P. Dale, Oct 01 2015 *)

Vec(-x*(x^2-5*x+1)*(x^2+14*x+1)/((x-1)*(x^2-10*x+1)*(x^2+10*x+1)) + O(x^100))

a(n) = a(n-1)+98*a(n-2)-98*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^2-5*x+1)*(x^2+14*x+1) / ((x-1)*(x^2-10*x+1)*(x^2+10*x+1)).

cp's OEIS Frontend

A253673 Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).

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