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 A020732 Pisot sequence T(4,7). 1
 4, 7, 12, 20, 33, 54, 88, 143, 232, 376, 609, 986, 1596, 2583, 4180, 6764, 10945, 17710, 28656, 46367, 75024, 121392, 196417, 317810, 514228, 832039, 1346268, 2178308, 3524577, 5702886, 9227464, 14930351, 24157816, 39088168, 63245985, 102334154, 165580140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n) = Fibonacci(n+5) - 1. a(n) = 2*a(n-1) - a(n-3). From Colin Barker, Mar 22 2016: (Start) a(n) = (-1+(2^(-1-n)*((1-sqrt(5))^n*(-11+5*sqrt(5))+(1+sqrt(5))^n*(11+5*sqrt(5))))/sqrt(5)). G.f.: (4-x-2*x^2) / ((1-x)*(1-x-x^2)). (End) MATHEMATICA Join[{a=4, b=7}, Table[c=a+b+1; a=b; b=c, {n, 0, 60}]] (* Vladimir Joseph Stephan Orlovsky, Nov 22 2010 *) PROG (PARI) Vec((4-x-2*x^2)/((1-x)*(1-x-x^2)) + O(x^50)) \\ Colin Barker, Mar 22 2016 CROSSREFS Subsequence of A000071. See A008776 for definitions of Pisot sequences. Sequence in context: A022809 A297554 A188554 * A339891 A310793 A117949 Adjacent sequences: A020729 A020730 A020731 * A020733 A020734 A020735 KEYWORD nonn,easy AUTHOR David W. Wilson STATUS approved

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Last modified May 23 08:52 EDT 2024. Contains 372760 sequences. (Running on oeis4.)