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A007667
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The sum of both two and three consecutive squares.
(Formerly M4037)
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8
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5, 365, 35645, 3492725, 342251285, 33537133085, 3286296790925, 322023548377445, 31555021444198565, 3092070077983081805, 302991312620897818205, 29690056566770003102165
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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).
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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).
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LINKS
| Index entries for sequences related to sums of squares
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FORMULA
| A007667 = 3*Square star numbers (A006061) + 2.
a(n) = 99(a(n-1) - a(n-2))+a(n-3); a(n)=3(5 - 2sqrt(6))/8*(sqrt(3) + sqrt(2))^(4n) + 3*(5 + 2sqrt(6))/8*(sqrt(3) - sqrt(2))^(4n) + 5/4
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EXAMPLE
| a(2) = 365 = 13^2+14^2 = 10^2+11^2+12^2.
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CROSSREFS
| Cf. A003154, A031138, A006061, A054320.
Sequence in context: A061456 A006430 A180766 * A121668 A160193 A098038
Adjacent sequences: A007664 A007665 A007666 * A007668 A007669 A007670
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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EXTENSIONS
| Additional comments from Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net) Feb 27 2000
Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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