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 A159675 Expansion of x*(1 + x)/(1 - 32*x + x^2). 3
 1, 33, 1055, 33727, 1078209, 34468961, 1101928543, 35227244415, 1126169892737, 36002209323169, 1150944528448671, 36794222701034303, 1176264181904649025, 37603659598247734497, 1202140842962022854879, 38430903315186483621631, 1228586765243005453037313 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 = 1..650 Index entries for linear recurrences with constant coefficients, signature (32,-1). FORMULA The a(j) recurrence is a(1)=1; a(2)=31; a(t+2)=32*a(t+1)-a(t) resulting in terms 1, 31, 991, 31681... (A159674). The b(j) recurrence is b(1)=1; b(2)=33; b(t+2)=32*b(t+1)-b(t) resulting in terms 1, 33, 1055, 33727... (this sequence). The n(j) recurrence is n(0)=n(1)=0; n(2)=64; n(t+3)=1023*(n(t+2)-n(t+1))+n(t) resulting in terms 0, 0, 64, 65472, 66912384... (A159677). G.f.: x*(1 + x)/(1 - 32*x + x^2). - Harvey P. Dale, Apr 22 2011 a(n) = (16+sqrt(255))^(-n)*(-15-sqrt(255)+(-15+sqrt(255))*(16+sqrt(255))^(2*n))/30. - 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 LinearRecurrence[{32, -1}, {1, 33}, 20] (* or *) CoefficientList[Series[(1+x)/(1-32 x+x^2), {x, 0, 20}], x] (* Harvey P. Dale, Apr 22 2011 *) PROG (PARI) Vec(x*(1+x)/(1-32*x+x^2) + O(x^20)) \\ Colin Barker, Feb 24 2014 (PARI) a(n) = round((16+sqrt(255))^(-n)*(-15-sqrt(255)+(-15+sqrt(255))*(16+sqrt(255))^(2*n))/30) \\ Colin Barker, Jul 25 2016 CROSSREFS Cf. A157456, A159674, A159677. Sequence in context: A197358 A299074 A101632 * A162837 A163216 A163567 Adjacent sequences:  A159672 A159673 A159674 * A159676 A159677 A159678 KEYWORD nonn,easy AUTHOR Paul Weisenhorn, Apr 19 2009 EXTENSIONS More terms from Harvey P. Dale, Apr 22 2011 New name from Colin Barker, Feb 24 2014 STATUS approved

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Last modified July 22 16:39 EDT 2019. Contains 325224 sequences. (Running on oeis4.)