A262077 The first of thirteen consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers.

15, 435, 66543, 1388283, 209496225, 4370333325, 659494068633, 13757807937693, 2076087118579335, 43309575017543115, 6535521589793696823, 136338528397417807203, 20573819888583439038345, 429193644085496239550805, 64766378473739076299032113

Offset

1,1

Comments

For the first of the corresponding seven consecutive positive integers, see A262076.

Links

Colin Barker, Table of n, a(n) for n = 1..572

Index entries for linear recurrences with constant coefficients, signature (1,3148,-3148,-1,1).

Formula

a(n) = a(n-1)+3148*a(n-2)-3148*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: 3*x*(9*x^4+140*x^3-6296*x^2-140*x-5) / ((x-1)*(x^4-3148*x^2+1)).

Example

15 is in the sequence because 15^2 + ... + 27^2 = 5915 = 26^2 + ... + 32^2.

Mathematica

LinearRecurrence[{1, 3148, -3148, -1, 1}, {15, 435, 66543, 1388283, 209496225}, 20] (* Vincenzo Librandi, Sep 11 2015 *)

Prog

(PARI) Vec(3*x*(9*x^4+140*x^3-6296*x^2-140*x-5)/((x-1)*(x^4-3148*x^2+1)) + O(x^20))
(Magma) I:=[15, 435, 66543, 1388283, 209496225]; [n le 5 select I[n] else Self(n-1)+3148*Self(n-2)-3148*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Sep 11 2015

Crossrefs

Cf. A262074, A262075, A262076.

Sequence in context: A323781 A253447 A302112 * A225492 A256194 A247141

Adjacent sequences: A262074 A262075 A262076 * A262078 A262079 A262080

Keyword

nonn,easy

Author

Colin Barker, Sep 10 2015

Status

approved