A279043 Numbers k such that 3*k+1 and 4*k+1 are both triangular numbers (A000217).

63, 12285, 2383290, 462346038, 89692748145, 17399930794155, 3375496881317988, 654828995044895580, 127033449541828424595, 24643834382119669475913, 4780776836681674049902590, 927446062481862646011626610, 179919755344644671652205659813

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..400

Index entries for linear recurrences with constant coefficients, signature (195,-195,1).

Formula

a(n) = 195*a(n-1) - 195*a(n-2) + a(n-3) for n>3.

G.f.: 63*x / ((1 - x)*(1 - 194*x + x^2)).

Example

63 is in the sequence because 3*63+1 = 190 and 4*63+1 = 253 are both triangular numbers.

Prog

(PARI) Vec(63*x / ((1 - x)*(1 - 194*x + x^2)) + O(x^20))
(PARI) isok(k) = ispolygonal(3*k+1, 3) & ispolygonal(4*k+1, 3)

Crossrefs

Cf. A000217, A274680.

Sequence in context: A174763 A160871 A183525 * A234629 A270507 A289875

Adjacent sequences: A279040 A279041 A279042 * A279044 A279045 A279046

Keyword

nonn,easy

Author

Colin Barker, Dec 04 2016

Status

approved