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 A202637 x-values in the solution to x^2 - 7*y^2 = -3. 2
 2, 5, 37, 82, 590, 1307, 9403, 20830, 149858, 331973, 2388325, 5290738, 38063342, 84319835, 606625147, 1343826622, 9667939010, 21416906117, 154080399013, 341326671250, 2455618445198, 5439809833883, 39135814724155, 86695630670878 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding values of y of this Pell equation are in A202638. LINKS Bruno Berselli, Table of n, a(n) for n = 1..1000 R. A. Mollin, Class Numbers of Quadratic Fields Determinet by Solvability of Diophantine Equations, Mathematics of Computation Vol. 48, 1987, p. 235 (Theorem 1.1, particular case). Index entries for linear recurrences with constant coefficients, signature (0,16,0,-1). FORMULA G.f.: x*(1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4). a(n) = -a(-n+1) = ((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2. a(2n)-a(2n-1) = A202638(2n)+A202638(2n-1). MATHEMATICA LinearRecurrence[{0, 16, 0, -1}, {2, 5, 37, 82}, 24] PROG (PARI) a=vector(24); a[1]=2; a[2]=5; a[3]=37; a[4]=82; for(i=5, #a, a[i]=16*a[i-2]-a[i-4]); a (Magma) m:=24; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x)*(2+3*x+2*x^2)/(1-16*x^2+x^4))); (Maxima) makelist(expand(((-2*(-1)^n+sqrt(7))*(8+3*sqrt(7))^floor(n/2)-(2*(-1)^n+sqrt(7))*(8-3*sqrt(7))^floor(n/2))/2), n, 1, 24); CROSSREFS Sequence in context: A106129 A163499 A086218 * A138658 A067464 A081545 Adjacent sequences: A202634 A202635 A202636 * A202638 A202639 A202640 KEYWORD nonn,easy AUTHOR Bruno Berselli, Dec 22 2011 STATUS approved

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Last modified December 4 19:34 EST 2023. Contains 367563 sequences. (Running on oeis4.)