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A279043 Numbers k such that 3*k+1 and 4*k+1 are both triangular numbers (A000217). 1
63, 12285, 2383290, 462346038, 89692748145, 17399930794155, 3375496881317988, 654828995044895580, 127033449541828424595, 24643834382119669475913, 4780776836681674049902590, 927446062481862646011626610, 179919755344644671652205659813 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 18:57 EDT 2019. Contains 324198 sequences. (Running on oeis4.)