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 A202638 y-values in the solution to x^2 - 7*y^2 = -3. 2
 1, 2, 14, 31, 223, 494, 3554, 7873, 56641, 125474, 902702, 1999711, 14386591, 31869902, 229282754, 507918721, 3654137473, 8094829634, 58236916814, 129009355423, 928136531551, 2056054857134, 14791947588002, 32767868358721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The corresponding values of x of this Pell equation are in A202637. 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)*(1+3*x+x^2)/(1-16*x^2+x^4). a(n) = a(-n+1) = ((7+2*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^floor(n/2)+(7-2*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^floor(n/2))/14. a(2n)+a(2n-1) = A202637(2n)-A202637(2n-1). MATHEMATICA LinearRecurrence[{0, 16, 0, -1}, {1, 2, 14, 31}, 24] PROG (PARI) a=vector(24); a[1]=1; a[2]=2; a[3]=14; a[4]=31; 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)*(1+3*x+x^2)/(1-16*x^2+x^4))); (Maxima) makelist(expand(((7+2*sqrt(7)*(-1)^n)*(8-3*sqrt(7))^floor(n/2)+(7-2*sqrt(7)*(-1)^n)*(8+3*sqrt(7))^floor(n/2))/14), n, 1, 24); CROSSREFS Sequence in context: A031301 A335200 A294558 * A226565 A231050 A337338 Adjacent sequences: A202635 A202636 A202637 * A202639 A202640 A202641 KEYWORD nonn,easy AUTHOR Bruno Berselli, Dec 22 2011 STATUS approved

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Last modified June 19 11:49 EDT 2024. Contains 373503 sequences. (Running on oeis4.)