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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 Index entries for linear recurrences with constant coefficients, signature (99,-99,1). 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 *) PROG (PARI) my(x='x+O('x^20)); Vec(5*x*(1-26*x+x^2)/((1-x)*(1-98*x+x^2))) \\ G. C. Greubel, Jul 23 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 5*x*(1-26*x+x^2)/((1-x)*(1-98*x+x^2)) )); // G. C. Greubel, Jul 23 2019 (Sage) (5*x*(1-26*x+x^2)/((1-x)*(1-98*x+x^2))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Jul 23 2019 (GAP) a:=[5, 365, 35645];; for n in [4..20] do a[n]:=99*a[n-1]-99*a[n-2] + a[n-3]; od; a; # G. C. Greubel, Jul 23 2019 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 October 21 04:26 EDT 2019. Contains 328291 sequences. (Running on oeis4.)