A254674 -id:A254674 - cp's OEIS frontend

A254675 Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).

1, 13, 44, 776, 2697, 48069, 167140, 2979472, 10359953, 184679165, 642149916, 11447128728, 39802934809, 709537301941, 2467139808212, 43979865591584, 152922865174305, 2726042129376237, 9478750500998668, 168970632155735080, 587529608196743081

Offset: 1

Colin Barker, Feb 05 2015

Also positive integers y in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of x being A254674.

			13 is in the sequence because the 13th centered triangular number is 235, which is also the 10th heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,62,-62,-1,1).

Cf. A000566, A005448, A254674, A254676.

Vec(x*(12*x^3+31*x^2-12*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))

a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(12*x^3+31*x^2-12*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).

A254676 Heptagonal numbers (A000566) which are also centered triangular numbers (A005448).

Original entry on oeis.org

1, 235, 2839, 902101, 10906669, 3465871039, 41903418691, 13315875628969, 160992923703385, 51159590700627091, 618534770964985711, 196555134155933653885, 2376410429054551397509, 755164774267506397598311, 9130168249892815504243099, 2901342866180625423639056209

Offset: 1

Colin Barker, Feb 05 2015

			235 is in the sequence because it is the 10th heptagonal number and the 13th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..558
Index entries for linear recurrences with constant coefficients, signature (1,3842,-3842,-1,1).

Cf. A000566, A005448, A254674, A254675.

LinearRecurrence[{1,3842,-3842,-1,1},{1,235,2839,902101,10906669},20] (* Harvey P. Dale, Oct 12 2024 *)

Vec(-x*(x^4+234*x^3-1238*x^2+234*x+1)/((x-1)*(x^2-62*x+1)*(x^2+62*x+1)) + O(x^100))

a(n) = a(n-1)+3842*a(n-2)-3842*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+234*x^3-1238*x^2+234*x+1) / ((x-1)*(x^2-62*x+1)*(x^2+62*x+1)).

cp's OEIS Frontend

A254675 Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).

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