A274579 Values of n such that 2*n+1 and 5*n+1 are both triangular numbers.

0, 1, 7, 27, 540, 2002, 10660, 39501, 779247, 2887450, 15372280, 56960982, 1123674201, 4163701465, 22166817667, 82137697110, 1620337419162, 6004054625647, 31964535704101, 118442502272205, 2336525434757970, 8657842606482076, 46092838318496542

Offset

1,3

Comments

Intersection of A074377 and A085787.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1442,-1442,0,0,-1,1).

Formula

G.f.: x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6) / ((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)).

Example

7 is in the sequence because 2*7+1 = 15, 5*7+1 = 36, and 15 and 36 are both triangular numbers.

Prog

(PARI) concat(0, Vec(x^2*(1+6*x+20*x^2+513*x^3+20*x^4+6*x^5+x^6)/((1-x)*(1+6*x-x^2)*(1-6*x-x^2)*(1+38*x^2+x^4)) + O(x^30)))
(PARI) isok(n) = ispolygonal(2*n+1, 3) && ispolygonal(5*n+1, 3); \\ Michel Marcus, Jun 29 2016

Crossrefs

Cf. A074377, A085787, A124174.

Sequence in context: A003148 A033910 A196647 * A152578 A300529 A299468

Adjacent sequences: A274576 A274577 A274578 * A274580 A274581 A274582

Keyword

nonn,easy

Author

Colin Barker, Jun 29 2016

Status

approved