A254285 -id:A254285 - cp's OEIS frontend

A254283 Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

1, 31, 115, 5965, 22261, 1157131, 4318471, 224477401, 837761065, 43547458615, 162521328091, 8447982493861, 31528299888541, 1638865056350371, 6116327657048815, 317931372949478065, 1186536037167581521, 61677047487142394191, 230181874882853766211

Offset: 1

Colin Barker, Jan 28 2015

Also positive integers x in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of y being A254284.

			31 is in the sequence because the 31st hexagonal number is 1891, which is also the 36th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..875
Index entries for linear recurrences with constant coefficients, signature (1,194,-194,-1,1).

Cf. A000384, A005448, A254284, A254285.

Vec(-x*(x^4+30*x^3-110*x^2+30*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+30*x^3-110*x^2+30*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).

A254284 Indices of centered triangular numbers (A005448) which are also hexagonal numbers (A000384).

Original entry on oeis.org

1, 36, 133, 6888, 25705, 1336140, 4986541, 259204176, 967363153, 50284273908, 187663465045, 9754889933880, 36405744855481, 1892398362898716, 7062526838498173, 367115527512416928, 1370093800923789985, 71218519939045985220, 265791134852376758821

Offset: 1

Colin Barker, Jan 28 2015

Also positive integers y in the solutions to 4*x^2 - 3*y^2 - 2*x + 3*y - 2 = 0, the corresponding values of x being A254283.

			36 is in the sequence because the 36th centered triangular number is 1891, which is also the 31st hexagonal number.

Colin Barker, Table of n, a(n) for n = 1..875
Index entries for linear recurrences with constant coefficients, signature (1,194,-194,-1,1).

Cf. A000384, A005448, A254283, A254285.

LinearRecurrence[{1,194,-194,-1,1},{1,36,133,6888,25705},20] (* Harvey P. Dale, Nov 11 2020 *)

Vec(x*(35*x^3+97*x^2-35*x-1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))

a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(35*x^3+97*x^2-35*x-1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).

cp's OEIS Frontend

A254283 Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

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