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A144930 Numbers k arising in A144929. 4
1, 109, 11989, 1318681, 145042921, 15953402629, 1754729246269, 193004263686961, 21228714276319441, 2334965566131451549, 256824983560183350949, 28248413226054037152841, 3107068629882383903461561, 341749300873836175343618869, 37589316027492096903894614029 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Numbers n such that there exists x in N : (x+1)^3 - x^3 = 7*n^2. - Richard Choulet, Oct 16 2008

LINKS

Colin Barker, Table of n, a(n) for n = 1..450

Index entries for linear recurrences with constant coefficients, signature (110,-1).

FORMULA

a(n+2) = 110*a(n+1)-a(n). - Richard Choulet, Oct 16 2008

a(n) = (1/2)*{[55+12*sqrt(21)]^n+[55-12*sqrt(21)]^n}+(3/28)*sqrt(21)*{[55+12*sqrt(21)]^n}-[55-12*sqrt(21)]^n } with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -x*(x-1) / (x^2-110*x+1). - Colin Barker, Oct 17 2014

EXAMPLE

a(1) = 1 because 2^3-1^3 = 7*1. - Richard Choulet, Oct 16 2008

MATHEMATICA

LinearRecurrence[{110, -1}, {1, 109}, 20] (* Harvey P. Dale, Oct 05 2016 *)

PROG

(PARI) Vec(-x*(x-1)/(x^2-110*x+1) + O(x^20)) \\ Colin Barker, Jul 14 2016

CROSSREFS

Cf. A144729, A144727.

Sequence in context: A278278 A280626 A227949 * A190827 A125044 A096209

Adjacent sequences:  A144927 A144928 A144929 * A144931 A144932 A144933

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Sep 25 2008

EXTENSIONS

More terms from Colin Barker, Oct 17 2014

STATUS

approved

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)