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 A161582 The list of the k values in the common solutions to the 2 equations 5*k+1=A^2, 9*k+1=B^2. 2
 0, 7, 336, 15792, 741895, 34853280, 1637362272, 76921173511, 3613657792752, 169764995085840, 7975341111241735, 374671267233275712, 17601574218852716736, 826899317018844410887, 38846666325666834594960, 1824966417989322381552240 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The 2 equations are equivalent to the Pell equation x^2-45*y^2=1, with x=(45*k+7)/2 and y= A*B/2, case C=5 in A160682. LINKS Table of n, a(n) for n=1..16. Index entries for linear recurrences with constant coefficients, signature (48,-48,1). FORMULA k(t+3) = 48*(k(t+2)-k(t+1))+k(t). With w = sqrt(5), k(t) = ((7+3*w)*((47+21*w)/2)^(t-1)+(7-3*w)*((47-21*w)/2)^(t-1))/90. k(t) = floor(((7+3*w)*((47+21*w)/2)^(t-1)/90) = 7*|A156093(t-1)|. G.f.: -7*x^2/((x-1)*(x^2-47*x+1)). a(1)=0, a(2)=7, a(3)=336, a(n) = 48*a(n-1)-48*a(n-2)+a(n-3). - Harvey P. Dale, Mar 21 2013 MAPLE t:=0: for n from 0 to 1000000 do a:=sqrt(5*n+1); b:=sqrt(9*n+1); if (trunc(a)=a) and (trunc(b)=b) then t:=t+1; print(t, n, a, b): end if: end do: MATHEMATICA LinearRecurrence[{48, -48, 1}, {0, 7, 336}, 30] (* or *) Rest[CoefficientList[ Series[ -7x^2/((x-1)(x^2-47x+1)), {x, 0, 30}], x]] (* Harvey P. Dale, Mar 21 2013 *) CROSSREFS Cf. A160682, A049685 (sequence of A), A033890 (sequence of B). Sequence in context: A009587 A281619 A054325 * A200967 A068150 A195803 Adjacent sequences: A161579 A161580 A161581 * A161583 A161584 A161585 KEYWORD nonn,easy AUTHOR Paul Weisenhorn, Jun 14 2009 EXTENSIONS Edited, extended by R. J. Mathar, Sep 02 2009 STATUS approved

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Last modified September 8 15:49 EDT 2024. Contains 375753 sequences. (Running on oeis4.)