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

1,2

Comments

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.

Links

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).

Formula

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)).

Example

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

Mathematica

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

Prog

(PARI) 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))

Crossrefs

Cf. A000384, A005448, A254283, A254285.

Sequence in context: A155708 A196891 A105090 * A076578 A044368 A044749

Adjacent sequences: A254281 A254282 A254283 * A254285 A254286 A254287

Keyword

nonn,easy

Author

Colin Barker, Jan 28 2015

Status

approved