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 A008845 Numbers k such that k+1 and k/2+1 are squares. 1
 0, 48, 1680, 57120, 1940448, 65918160, 2239277040, 76069501248, 2584123765440, 87784138523760, 2982076586042448, 101302819786919520, 3441313796169221280, 116903366249966604048, 3971273138702695316400, 134906383349641674153600, 4582845760749114225906048 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 256. LINKS Colin Barker, Table of n, a(n) for n = 0..650 Henry Ernest Dudeney, Amusements in Mathematics, 1917. See problem 114, "Curious numbers". Index entries for linear recurrences with constant coefficients, signature (35,-35,1). FORMULA a(n) = 2*(A008844(n)-1) = 16*A075528(n) = 48*A029546(n). - corrected by Sean A. Irvine, Apr 07 2018 a(0)=0, a(1)=48, a(2)=1680, a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3). - Harvey P. Dale, May 24 2014 From Colin Barker, Mar 02 2016: (Start) a(n) = (-6+(3-2*sqrt(2))*(17+12*sqrt(2))^(-n)+(3+2*sqrt(2))*(17+12*sqrt(2))^n)/4. G.f.: 48*x / ((1-x)*(1-34*x+x^2)). (End) a(n) = 34*a(n-1) - a(n-2) + 48. - Vincenzo Librandi, Mar 03 2016 EXAMPLE 48+1 = 49 = 7^2 and 48/2+1 = 24+1 = 25 = 5^2. MAPLE seq(coeff(series(48*x/((1-x)*(1-34*x+x^2)), x, n+1), x, n), n = 0..20); # G. C. Greubel, Sep 13 2019 MATHEMATICA LinearRecurrence[{35, -35, 1}, {0, 48, 1680}, 20] (* Harvey P. Dale, May 24 2014 *) PROG (PARI) concat(0, Vec(48*x/((1-x)*(1-34*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 02 2016 (MAGMA) I:=[0, 48]; [n le 2 select I[n] else  34*Self(n-1) - Self(n-2)+48: n in [1..20]]; // Vincenzo Librandi, Mar 03 2016 (Sage) def A008845_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P(48*x/((1-x)*(1-34*x+x^2))).list() A008845_list(20) # G. C. Greubel, Sep 13 2019 (GAP) a:=[0, 48, 1680];; for n in [4..20] do a[n]:=35*a[n-1]-35*a[n-2] +a[n-3]; od; a; # G. C. Greubel, Sep 13 2019 CROSSREFS Sequence in context: A266160 A004386 A076003 * A273627 A288455 A231450 Adjacent sequences:  A008842 A008843 A008844 * A008846 A008847 A008848 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 15 06:12 EDT 2021. Contains 342975 sequences. (Running on oeis4.)