A319172 a(n) = 2*(a(n-1) + a(n-3)) - a(n-4), with a(0) = 1, a(1) = 2, a(2) = 5 and a(3) = 12.
1, 2, 5, 12, 27, 62, 143, 328, 753, 1730, 3973, 9124, 20955, 48126, 110527, 253840, 582977, 1338882, 3074917, 7061948, 16218683, 37248318, 85545615, 196466648, 451211249, 1036265410, 2379918501, 5465792852, 12552905275, 28829382142
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,2,-1).
Crossrefs
Cf. A319129.
Programs
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GAP
a:=[1,2,5,12];; for n in [5..30] do a[n]:=2*(a[n-1]+a[n-3])-a[n-4]; od; a; # Muniru A Asiru, Sep 12 2018
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Magma
I:=[1,2,5,12]; [n le 4 select I[n] else 2*(Self(n-1) + Self(n-3)) - Self(n-4): n in [1..30]]; // Vincenzo Librandi, Sep 29 2018
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Maple
f:= gfun:-rectoproc({a(n) = 2*(a(n-1)+a(n-3))-a(n-4), a(0) = 1, a(1) = 2, a(2) = 5, a(3) = 12},a(n),remember): map(f, [$0..40]); # Robert Israel, Sep 12 2018 -
Mathematica
LinearRecurrence[{2, 0, 2, -1}, {1, 2, 5, 12}, 30] (* Vincenzo Librandi, Sep 29 2018 *) CoefficientList[Series[(1 + x^2) / (1 - 2*x - 2*x^3 + x^4), {x, 0, 30}], x] (* Stefano Spezia, Sep 29 2018 *) -
PARI
Vec((1 + x^2) / (1 - 2*x - 2*x^3 + x^4) + O(x^40)) \\ Colin Barker, Sep 13 2018
Formula
Limit_{n -> inf} a(n)/a(n-1) = (1 + sqrt(3) + sqrt(2*sqrt(3)))/2 = A319129.
G.f.: (1 + x^2) / (1 - 2*x - 2*x^3 + x^4). - Colin Barker, Sep 13 2018
Comments