A274587 Values of n such that 2*n-1 and 4*n-1 are both triangular numbers.

1, 23, 176, 5968, 888778, 30192278, 233944673, 7947232183, 1183597668523, 40207478867501, 311547395822378, 10583440358908726, 1576213585538112676, 53544862512524597468, 414892028679967914251, 14094115694115827467213, 2099065698850118586101173

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..650

Index entries for linear recurrences with constant coefficients, signature (35,-1189,40391,-40391,1189,-35,1).

Formula

Intersection of A174114 and A213399.

G.f.: x*(1-12*x+560*x^2-13236*x^3+560*x^4-12*x^5+x^6) / ((1-x)*(1-34*x+x^2)*(1+1154*x^2+x^4)).

Example

23 is in the sequence because 2*23-1 = 45, 4*23-1 = 91, and 45 and 91 are both triangular numbers.

Mathematica

Rest@ CoefficientList[Series[x (1 - 12 x + 560 x^2 - 13236 x^3 + 560 x^4 - 12 x^5 + x^6)/((1 - x) (1 - 34 x + x^2) (1 + 1154 x^2 + x^4)), {x, 0, 17}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{35, -1189, 40391, -40391, 1189, -35, 1}, {1, 23, 176, 5968, 888778, 30192278, 233944673}, 20] (* Harvey P. Dale, Jan 18 2021 *)

Prog

(PARI) isok(n) = ispolygonal(2*n-1, 3) && ispolygonal(4*n-1, 3)
(PARI) Vec(x*(1-12*x+560*x^2-13236*x^3+560*x^4-12*x^5+x^6)/((1-x)*(1-34*x+x^2)*(1+1154*x^2+x^4)) + O(x^20))

Crossrefs

Cf. A174114, A213399, A274588.

Sequence in context: A248698 A186260 A229426 * A302200 A269072 A125360

Adjacent sequences: A274584 A274585 A274586 * A274588 A274589 A274590

Keyword

nonn,easy

Author

Colin Barker, Jun 29 2016

Status

approved