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A180920 Number a(n) of terms in the sum of cube of consecutive integers starting from a(n) such that the sum equals a squared integer. 2
1, 33, 2017, 124993, 7747521, 480221281, 29765971873, 1845010034817, 114360856186753, 7088528073543841, 439374379703531361, 27234123013545400513, 1688076252460111300417, 104633493529513355225313, 6485588522577367912668961, 402001854906267297230250241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..558

V. Pletser, General solutions of sums of consecutive cubed integers equal to squared integers, arXiv:1501.06098 [math.NT], 2015.

FORMULA

a(n) = 31*a(n-1) - 14 + 8*((3*a(n-1) - 1)*(5*a(n-1) - 3))^(1/2).

Conjectures from Colin Barker, Feb 18 2015: (Start)

a(n) = 63*a(n-1)-63*a(n-2)+a(n-3).

G.f.: -x*(x^2-30*x+1) / ((x-1)*(x^2-62*x+1)).

(End)

MATHEMATICA

a[1] = 1; a[n_] := a[n] = 31 a[n - 1] - 14 + 8 Sqrt[(3 a[n - 1] - 1)*(5 a[n - 1] - 3)]; Array[a, 14] (* Robert G. Wilson v, Sep 27 2010 *)

PROG

(PARI)

default(realprecision, 1000)

vector(20, n, if(n==1, t=1, t=round(31*t-14+8*((3*t-1)*(5*t-3))^(1/2)))) \\ Colin Barker, Feb 19 2015

CROSSREFS

Cf. A180921.

Sequence in context: A284164 A284221 A264170 * A120288 A284112 A099370

Adjacent sequences:  A180917 A180918 A180919 * A180921 A180922 A180923

KEYWORD

nonn,easy

AUTHOR

Vladimir Pletser, Sep 24 2010

EXTENSIONS

a(8) onwards from Robert G. Wilson v, Sep 27 2010

STATUS

approved

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Last modified March 29 08:58 EDT 2017. Contains 284268 sequences.