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A274579 Values of n such that 2*n+1 and 5*n+1 are both triangular numbers. 6
0, 1, 7, 27, 540, 2002, 10660, 39501, 779247, 2887450, 15372280, 56960982, 1123674201, 4163701465, 22166817667, 82137697110, 1620337419162, 6004054625647, 31964535704101, 118442502272205, 2336525434757970, 8657842606482076, 46092838318496542 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 18:10 EST 2019. Contains 329901 sequences. (Running on oeis4.)