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A145210 Numbers n such that there exists x in N : (x+1)^3-x^3=67*n^2. 2
31, 31935859, 32900002583179, 33893253661133238151, 34916490989129950608195511, 35970619852057890563395800238939, 37056572865356601788515589497544372899, 38175310800125746976658817253911841716581871, 39327823433144486705018790345018924628507933312591 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..170

Index entries for linear recurrences with constant coefficients, signature (1030190,-1).

FORMULA

a(n+2) = 1030190*a(n+1)-a(n).

a(n) = (31/2)*{[515095+124*sqrt(17255649)]^n+[515095-124*sqrt(17255649)]^n}-(1/268)*sqrt(17255649)*{[515095-124 *sqrt(17255649)]^n-[515095+124*sqrt(17255649)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

a(n) = A145207(n)/4489. - Colin Barker, Oct 19 2014

G.f.: -31*x*(x-1) / (x^2-1030190*x+1). - Colin Barker, Oct 19 2014

EXAMPLE

a(1)=31 because the first relation is : 147^3-146^3=67*31^2.

MATHEMATICA

CoefficientList[Series[31 (1 - x)/(x^2 - 1030190 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 19 2014 *)

PROG

(PARI) Vec(-31*x*(x-1)/(x^2-1030190*x+1) + O(x^20)) \\ Colin Barker, Oct 19 2014

(MAGMA) I:=[31, 31935859]; [n le 2 select I[n] else 1030190*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi, Oct 19 2014

CROSSREFS

Sequence in context: A051155 A216791 A324268 * A091308 A023927 A240253

Adjacent sequences:  A145207 A145208 A145209 * A145211 A145212 A145213

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 04 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 19 2014

STATUS

approved

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)