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A261974 The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers. 3
67, 3307, 152275, 7001563, 321919843, 14801311435, 680538406387, 31289965382587, 1438657869192835, 66146972017488043, 3041322054935257363, 139834667555004350875, 6429353385475264883107, 295610421064307180272267, 13591650015572655027641395 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the first of the corresponding three consecutive positive integers, see A261973.

LINKS

Colin Barker, Table of n, a(n) for n = 1..601

Index entries for linear recurrences with constant coefficients, signature (47,-47,1).

FORMULA

a(n) = 47*a(n-1)-47*a(n-2)+a(n-3) for n>3.

G.f.: x*(5*x^2-158*x-67) / ((x-1)*(x^2-46*x+1)).

a(n) = -5+3*sqrt(3/11)*(23+4*sqrt(33))^(-n)*(-1+(23+4*sqrt(33))^(2*n)). - Colin Barker, Mar 03 2016

EXAMPLE

67 is in the sequence because 67^2 + ... + 77^2 = 57134 = 137^2 + 138^2 + 139^2.

MATHEMATICA

LinearRecurrence[{47, -47, 1}, {67, 3307, 152275}, 20] (* Harvey P. Dale, Jul 02 2016 *)

PROG

(PARI) Vec(x*(5*x^2-158*x-67)/((x-1)*(x^2-46*x+1)) + O(x^40))

CROSSREFS

Cf. A157088, A261972, A261973.

Sequence in context: A069397 A103727 A120663 * A078989 A156121 A280004

Adjacent sequences:  A261971 A261972 A261973 * A261975 A261976 A261977

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 07 2015

STATUS

approved

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Last modified November 14 14:43 EST 2019. Contains 329126 sequences. (Running on oeis4.)