A020732 Pisot sequence T(4,7).

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

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Dominika Závacká, Cristina Dalfó, and Miquel Angel Fiol, Integer sequences from k-iterated line digraphs, CEUR: Proc. 24th Conf. Info. Tech. - Appl. and Theory (ITAT 2024) Vol 3792, 156-161. See p. 161, Table 2.

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