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A251625 Numbers n such that the octagonal number N(n) is the sum of three consecutive octagonal numbers. 2
483, 1304163, 3523847043, 9521433405123, 25726909536794403, 69514100046985070883, 187827072600044124730563, 507508680651219178036909443, 1371288267292521619011604583523, 3705220390715712763350177547768803, 10011504124425588594050560722466721283 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also nonnegative integers y in the solutions to 18*x^2-6*y^2+24*x+4*y+18 = 0, the corresponding values of x being A251624.

It seems that the least significant digit of each term is 3.

LINKS

Colin Barker, Table of n, a(n) for n = 1..291

Index entries for linear recurrences with constant coefficients, signature (2703,-2703,1).

FORMULA

a(n) = 2703*a(n-1)-2703*a(n-2)+a(n-3).

G.f.: -3*x*(x^2-462*x+161) / ((x-1)*(x^2-2702*x+1)).

a(n) =  (1 + 2*(sqrt(3)+2)*(1351+780*sqrt(3))^(-n) - 2*(sqrt(3)-2)*(1351+780*sqrt(3))^n) / 3. - Colin Barker, May 30 2017

EXAMPLE

483 is in the sequence because N(483) = 698901 = 231296+232965+234640 = N(278)+N(279)+N(280).

PROG

(PARI) Vec(-3*x*(x^2-462*x+161)/((x-1)*(x^2-2702*x+1)) + O(x^100))

CROSSREFS

Cf. A000567, A251624.

Sequence in context: A281047 A158330 A288082 * A156646 A177434 A202444

Adjacent sequences:  A251622 A251623 A251624 * A251626 A251627 A251628

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Dec 06 2014

STATUS

approved

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Last modified January 22 13:21 EST 2021. Contains 340362 sequences. (Running on oeis4.)