A274587 - OEIS

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

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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

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