A262139 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.

22, 145, 862, 5041, 29398, 171361, 998782, 5821345, 33929302, 197754481, 1152597598, 6717831121, 39154389142, 228208503745, 1330096633342, 7752371296321, 45184131144598, 263352415571281, 1534930362283102, 8946229758127345, 52142448186480982

Offset

1,1

Comments

For the first of the corresponding nine consecutive positive integers, see A262140.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>3.

G.f.: -x*(x^2-9*x+22) / ((x-1)*(x^2-6*x+1)).

a(n) = (-14+3*(3-2*sqrt(2))^(1+n)+3*(3+2*sqrt(2))^(1+n))/4. - Colin Barker, Mar 05 2016

Example

22 is in the sequence because 22^2 + ... + 29^2 = 5244 = 20^2 + ... + 28^2.

Mathematica

LinearRecurrence[{7, -7, 1}, {22, 145, 862}, 30] (* Harvey P. Dale, Apr 19 2016 *)

Prog

(PARI) Vec(-x*(x^2-9*x+22)/((x-1)*(x^2-6*x+1)) + O(x^40))

Crossrefs

Cf. A262140.

Sequence in context: A126490 A200776 A169722 * A159505 A223836 A224144

Adjacent sequences: A262136 A262137 A262138 * A262140 A262141 A262142

Keyword

nonn,easy

Author

Colin Barker, Sep 12 2015

Status

approved