The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A262075 The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers. 4
 105, 3248, 97433, 2919840, 87497865, 2622016208, 78572988473, 2354567638080, 70558456154025, 2114399116982768, 63361415053329113, 1898728052482890720, 56898480159433392585, 1705055676730518886928, 51094771821756133215353, 1531138098975953477573760 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For the first of the corresponding seven consecutive positive integers, see A262074. LINKS Colin Barker, Table of n, a(n) for n = 1..676 Index entries for linear recurrences with constant coefficients, signature (31,-31,1). FORMULA a(n) = 31*a(n-1)-31*a(n-2)+a(n-3) for n>3. G.f.: 7*x*(x-15) / ((x-1)*(x^2-30*x+1)). EXAMPLE 105 is in the sequence because 105^2 + ... + 112^2 (8 terms) = 94220 = 113^2 + ... + 119^2 (7 terms). MATHEMATICA LinearRecurrence[{31, -31, 1}, {105, 3248, 97433}, 20] (* Vincenzo Librandi, Sep 11 2015 *) Table[1/4 (-14-(15-4 Sqrt[14])^n (7+2 Sqrt[14])+(-7+2 Sqrt[14]) (15+4 Sqrt[ 14])^n), {n, 2, 20}]//Simplify (* Harvey P. Dale, Aug 01 2019 *) PROG (PARI) Vec(7*x*(x-15)/((x-1)*(x^2-30*x+1)) + O(x^20)) (MAGMA) I:=[105, 3248, 97433]; [n le 3 select I[n] else 31*Self(n-1)-31*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Sep 11 2015 CROSSREFS Cf. A262074, A262076, A262077. Sequence in context: A220822 A166821 A166803 * A018233 A154633 A122814 Adjacent sequences:  A262072 A262073 A262074 * A262076 A262077 A262078 KEYWORD nonn,easy AUTHOR Colin Barker, Sep 10 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)