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 A159677 Expansion of 64*x^2/(-x^3 + 1023*x^2 - 1023*x + 1). 3
 0, 0, 64, 65472, 66912384, 68384391040, 69888780730560, 71426265522241344, 72997573474949923072, 74603448665133299138304, 76244651538192756769423680, 77921959268584332285051862720, 79636166127841649402566234276224, 81388083860694897105090406378438272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Previous name was: The general form of the recurrences are the a(j), b(j) and n(j) solutions of the 2 equations problem: 15*n(j)+1=a(j)*a(j) and 17*n(j)+1=b(j)*b(j) with positive integer numbers. LINKS Colin Barker, Table of n, a(n) for n = 0..300 Index entries for linear recurrences with constant coefficients, signature (1023,-1023,1). FORMULA The a(j) recurrence is a(0)=1; a(1)=31; a(t+2)=32*a(t+1)-a(t) resulting in terms 1, 31, 991, 31681... (A159674) The b(j) recurrence is b(0)=1; b(1)=33; b(t+2)=32*b(t+1)-b(t) resulting in terms 1, 33, 1055, 33727... (A159675) The n(j) recurrence is n(-1)=n(0)=0; n(1)=64; n(t+3)=1023*(n(t+2)-n(t+1))+n(t) resulting in terms 0, 0, 64, 65472, 66912384... (this sequence). a(n) = -((511+32*sqrt(255))^(-n)*(-1+(511+32*sqrt(255))^n)*(16+sqrt(255)+(-16+sqrt(255))*(511+32*sqrt(255))^n))/510. - Colin Barker, Jul 25 2016 MAPLE for a from 1 by 2 to 100000 do b:=sqrt((17*a*a-2)/15): if (trunc(b)=b) then n:=(a*a-1)/15: La:=[op(La), a]:Lb:=[op(Lb), b]:Ln:=[op(Ln), n]: endif: enddo: MATHEMATICA RecurrenceTable[{a[0]==a[1]==0, a[2]==64, a[n]==1023(a[n-1]-a[n-2])+ a[n-3]}, a, {n, 20}] (* Harvey P. Dale, Jan 01 2014 *) LinearRecurrence[{1023, -1023, 1}, {0, 0, 64}, 20] (* Harvey P. Dale, Jan 01 2014 *) PROG (PARI) concat([0, 0], Vec(64/(-x^3+1023*x^2-1023*x+1) + O(x^20))) \\ Colin Barker, Mar 04 2014 (PARI) a(n) = round(-((511+32*sqrt(255))^(-n)*(-1+(511+32*sqrt(255))^n)*(16+sqrt(255)+(-16+sqrt(255))*(511+32*sqrt(255))^n))/510) \\ Colin Barker, Jul 25 2016 (MAGMA) I:=[0, 0, 64]; [n le 3 select I[n] else 1023*Self(n-1) - 1023*Self(n-2) +Self(n-3): n in [1..30]]; // G. C. Greubel, Jun 03 2018 CROSSREFS Cf. A157456, A159674, A159675. Sequence in context: A123394 A069445 A227604 * A013832 A320862 A034989 Adjacent sequences:  A159674 A159675 A159676 * A159678 A159679 A159680 KEYWORD nonn,easy AUTHOR Paul Weisenhorn, Apr 19 2009 EXTENSIONS More terms from Harvey P. Dale, Jan 01 2014 New name from Colin Barker, Feb 24 2014 Offset changed to 0 by Colin Barker, Mar 04 2014 STATUS approved

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Last modified July 17 23:21 EDT 2019. Contains 325109 sequences. (Running on oeis4.)