A254283 -id:A254283 - cp's OEIS frontend

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

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)).

A254285 Hexagonal numbers (A000384) which are also centered triangular numbers (A005448).

Original entry on oeis.org

1, 1891, 26335, 71156485, 991081981, 2677903145191, 37298379237211, 100780206894952201, 1403687203222107385, 3792762303606727977835, 52826364168762410080471, 142736816433155393822880781, 1988067387723517337746328821, 5371757345852607787523567324911

Offset: 1

Colin Barker, Jan 28 2015

			1891 is in the sequence because it is the 31st hexagonal number and the 36th centered triangular number.

Colin Barker, Table of n, a(n) for n = 1..437
Index entries for linear recurrences with constant coefficients, signature (1,37634,-37634,-1,1).

Cf. A000384, A005448, A254283, A254284.

Vec(-x*(x^4+1890*x^3-13190*x^2+1890*x+1)/((x-1)*(x^2-194*x+1)*(x^2+194*x+1)) + O(x^100))

a(n) = a(n-1)+37634*a(n-2)-37634*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+1890*x^3-13190*x^2+1890*x+1) / ((x-1)*(x^2-194*x+1)*(x^2+194*x+1)).

cp's OEIS Frontend

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

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