A253822 -id:A253822 - cp's OEIS frontend

A253821 Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448).

1, 181, 589, 208489, 679321, 240595741, 783935461, 277647276241, 904660842289, 320404716185989, 1043977828065661, 369746764831354681, 1204749508926930121, 426687446210667115501, 1390279889323849293589, 492396943180345019933089, 1604381787530213157871201

Offset: 1

Colin Barker, Jan 14 2015

Also positive integers x in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of y being A253822.

			181 is in the sequence because the 181st octagonal number is 97921, which is also the 256th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..653
Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Cf. A000567, A005448, A253822, A253823.

Vec(-x*(x^4+180*x^3-746*x^2+180*x+1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+180*x^3-746*x^2+180*x+1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

A253823 Octagonal numbers (A000567) which are also centered triangular numbers (A005448).

Original entry on oeis.org

1, 97921, 1039585, 130402572385, 1384429704481, 173658931280825761, 1843664419471976641, 231264030011583194717761, 2455233718711319470593985, 307977546462671843639087352385, 3269669116478082433043125969441, 410138010309759307549971991199125921

Offset: 1

Colin Barker, Jan 14 2015

			97921 is in the sequence because it is the 181st octagonal number and the 256th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..327
Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-1,1).

Cf. A000567, A005448, A253821, A253822.

LinearRecurrence[{1,1331714,-1331714,-1,1},{1,97921,1039585,130402572385,1384429704481},20] (* Harvey P. Dale, Jan 22 2025 *)

Vec(-x*(x^4+97920*x^3-390050*x^2+97920*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))

a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+97920*x^3-390050*x^2+97920*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).

cp's OEIS Frontend

A253821 Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448).

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