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A145322 Numbers n such that there exists x in N : (x+1)^3-x^3=31*n^2. 0
7, 170107, 4133940307, 100463017170607, 2441452239146151007, 59332172215266744601507, 1441890446733960188159672107, 35040821577196528277389606942807, 851562044527139583463162039764423607, 20694660771057724580125235612965415554507 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..10.

Index entries for linear recurrences with constant coefficients, signature (24302,-1).

FORMULA

a(n+2) = 24302*a(n+1)-a(n).

a(n) = (45/124)*sqrt(93)*{[12151+1260*sqrt(93)]^n-[12151-1260*sqrt(93)]^n}+(7/2)*{[12151+1260*sqrt(93)]^n+[12151-1260*sqrt(93)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -7*x*(x-1) / (x^2-24302*x+1). - Colin Barker, Oct 19 2014

EXAMPLE

a(1)=7 because 23^3-22^3=31*7^2.

PROG

(PARI) Vec(-7*x*(x-1)/(x^2-24302*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014

CROSSREFS

Sequence in context: A243859 A297059 A306256 * A145335 A003835 A138878

Adjacent sequences:  A145319 A145320 A145321 * A145323 A145324 A145325

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 07 2008

EXTENSIONS

Editing and a(10) from Colin Barker, Oct 19 2014

STATUS

approved

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Last modified May 26 07:44 EDT 2019. Contains 323579 sequences. (Running on oeis4.)