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 A059989 Numbers n such that 3*n+1 and 4*n+1 are both squares. 4
 0, 56, 10920, 2118480, 410974256, 79726887240, 15466605150360, 3000441672282656, 582070217817684960, 112918621814958599640, 21905630561884150645256, 4249579410383710266580080, 824396499983877907565890320, 159928671417461930357516142056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..400 Index entries for linear recurrences with constant coefficients, signature (195,-195,1). FORMULA a(n) = (A001570(n)^2 - 1)/3. G.f.: 56*x^2 / (1-195*x+195*x^2-x^3). From Colin Barker, Mar 03 2016: (Start) a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n>3. a(n) = (-1)*((97+56*sqrt(3))^(-n)*(-1+(97+56*sqrt(3))^n)*(7+4*sqrt(3)+(-7+4*sqrt(3))*(97+56*sqrt(3))^n))/48. (End) EXAMPLE 3*56+1=13^2 and 4*56+1=15^2. MAPLE f:= proc(n) local u; u:= <<7, 8>|<6, 7>>^n . <1, -1>; (u[1]^2-1)/3 end proc: map(f, [\$1..30]); # Robert Israel, Mar 03 2016 MATHEMATICA CoefficientList[Series[56 x/(1 - 195 x + 195 x^2 - x^3), {x, 0, 13}], x] (* Michael De Vlieger, Mar 03 2016 *) PROG (PARI) isok(n) = issquare(3*n+1) && issquare(4*n+1) \\ Michel Marcus, Jun 08 2013 (PARI) concat(0, Vec(56*x^2/((1-x)*(1-194*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 03 2016 CROSSREFS Cf. A245031. Sequence in context: A034204 A275921 A091546 * A352602 A184125 A213865 Adjacent sequences: A059986 A059987 A059988 * A059990 A059991 A059992 KEYWORD nonn,easy AUTHOR David Radcliffe, Mar 07 2001 EXTENSIONS Offset changed to 1 by Joerg Arndt, Mar 03 2016 STATUS approved

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Last modified March 25 23:47 EDT 2023. Contains 361529 sequences. (Running on oeis4.)