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A261972 The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers. 3
25, 361, 5041, 70225, 978121, 13623481, 189750625, 2642885281, 36810643321, 512706121225, 7141075053841, 99462344632561, 1385331749802025, 19295182152595801, 268747218386539201, 3743165875258953025, 52135575035238803161, 726154884618084291241 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the first of the corresponding four consecutive positive integers, see A157088.

LINKS

Colin Barker, Table of n, a(n) for n = 1..873

Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

FORMULA

a(n) = 15*a(n-1)-15*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x^2-14*x+25) / ((x-1)*(x^2-14*x+1)).

a(n) = (-2-(7-4*sqrt(3))^n*(-2+sqrt(3))+(2+sqrt(3))*(7+4*sqrt(3))^n)/2. - Colin Barker, Mar 05 2016

EXAMPLE

25 is in the sequence because 25^2 + 26^2 + 27^2 = 2030 = 21^2 + 22^2 + 23^2 + 24^2.

PROG

(PARI) Vec(-x*(x^2-14*x+25)/((x-1)*(x^2-14*x+1)) + O(x^40))

CROSSREFS

Cf. A157088, A261973, A261974.

Sequence in context: A188487 A306083 A077512 * A197678 A197536 A045622

Adjacent sequences:  A261969 A261970 A261971 * A261973 A261974 A261975

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 07 2015

STATUS

approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)