login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A007667 The sum of both two and three consecutive squares.
(Formerly M4037)
8
5, 365, 35645, 3492725, 342251285, 33537133085, 3286296790925, 322023548377445, 31555021444198565, 3092070077983081805, 302991312620897818205, 29690056566770003102165 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = (b(n)-1)^2+b(n)^2+(b(n)+1)^2 = c(n)^2+(c(n)+1)^2, where b(n) is A054320 and c(n) is A031138; a(n) = 3b(n)+2, where b(n) is a Star square number (A006061).

REFERENCES

M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 22.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Index entries for sequences related to sums of squares

FORMULA

A007667 = 3*Square star numbers (A006061) + 2.

a(n) = 99*(a(n-1) - a(n-2))+a(n-3); a(n)=3*(5 - 2*sqrt(6))/8*(sqrt(3) + sqrt(2))^(4*n) + 3*(5 + 2*sqrt(6))/8*(sqrt(3) - sqrt(2))^(4*n) + 5/4.

G.f.: 5*x*(1-26*x+x^2)/((1-x)*(1-98*x+x^2)). [Colin Barker, Apr 14 2012]

EXAMPLE

a(2) = 365 = 13^2+14^2 = 10^2+11^2+12^2.

MATHEMATICA

CoefficientList[Series[5*(1-26*x+x^2)/((1-x)*(1-98*x+x^2)), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 16 2012 *)

CROSSREFS

Cf. A003154, A031138, A006061, A054320.

Sequence in context: A218994 A006430 A180766 * A247082 A121668 A234311

Adjacent sequences:  A007664 A007665 A007666 * A007668 A007669 A007670

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

Additional comments from Ignacio Larrosa CaƱestro Feb 27 2000

Corrected by T. D. Noe, Nov 07 2006

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified September 26 05:09 EDT 2017. Contains 292502 sequences.