A274588 Values of n such that 2*n-1 and 7*n-1 are both triangular numbers.

1, 8, 638, 6931, 572671, 6223778, 514257668, 5588945461, 461802812941, 5018866799948, 414698411763098, 4506936797407591, 372398711960448811, 4047224225205216518, 334413628642071268928, 3634402847297487025321, 300303066121868039048281

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,898,-898,-1,1).

Formula

Intersection of A069099 and A174114.

G.f.: (1+7*x-268*x^2+7*x^3+x^4) / ((1-x)*(1-30*x+x^2)*(1+30*x+x^2)).

Example

8 is in the sequence because 2*8-1 = 15, 7*8-1 = 55, and 15 and 55 are both triangular numbers.

Mathematica

CoefficientList[Series[(1 + 7 x - 268 x^2 + 7 x^3 + x^4)/((1 - x) (1 - 30 x + x^2) (1 + 30 x + x^2)), {x, 0, 16}], x] (* Michael De Vlieger, Jun 30 2016 *)
LinearRecurrence[{1, 898, -898, -1, 1}, {1, 8, 638, 6931, 572671}, 20] (* Harvey P. Dale, Apr 10 2023 *)

Prog

(PARI) isok(n) = ispolygonal(2*n-1, 3) && ispolygonal(7*n-1, 3)
(PARI) Vec((1+7*x-268*x^2+7*x^3+x^4)/((1-x)*(1-30*x+x^2)*(1+30*x+x^2)) + O(x^20))

Crossrefs

Cf. A069099, A174114, A274587.

Sequence in context: A266317 A080320 A083942 * A027877 A129927 A196800

Adjacent sequences: A274585 A274586 A274587 * A274589 A274590 A274591

Keyword

nonn,easy

Author

Colin Barker, Jun 29 2016

Status

approved