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 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 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: A006430 A301613 A180766 * A247082 A121668 A234311 Adjacent sequences:  A007664 A007665 A007666 * A007668 A007669 A007670 KEYWORD nonn,easy AUTHOR EXTENSIONS Additional comments from Ignacio Larrosa CaĆ±estro Feb 27 2000 Corrected by T. D. Noe, Nov 07 2006 STATUS approved

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Last modified December 18 20:06 EST 2018. Contains 318245 sequences. (Running on oeis4.)