A320933 a(n) = 2^n - floor((n+3)/2).
0, 0, 2, 5, 13, 28, 60, 123, 251, 506, 1018, 2041, 4089, 8184, 16376, 32759, 65527, 131062, 262134, 524277, 1048565, 2097140, 4194292, 8388595, 16777203, 33554418, 67108850, 134217713, 268435441, 536870896
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- OEIS Wiki, Autosequence
- Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).
Programs
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GAP
List([0..40],n->2^n-Int((n+3)/2)); # Muniru A Asiru, Oct 28 2018
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Magma
[((-1)^n+2^(n+2)-2*n-5)/4: n in [0..40]]; // G. C. Greubel, Jun 04 2019
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Maple
seq(2^n-floor((n+3)/2),n=0..40); # Muniru A Asiru, Oct 28 2018
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Mathematica
a[n_]:=2^n - Floor[(n+3)/2]; Array[a, 40, 0] (* or *) CoefficientList[ Series[x^2*(2-x)/((1-x)^2*(1-x-2*x^2)), {x, 0, 40}], x] (* Stefano Spezia, Oct 28 2018 *) -
PARI
concat([0,0], Vec(x^2*(2-x)/((1-x)^2*(1+x)*(1-2*x)) + O(x^40))) \\ Colin Barker, Oct 28 2018
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Sage
[((-1)^n+2^(n+2)-2*n-5)/4 for n in (0..40)] # G. C. Greubel, Jun 04 2019
Formula
a(n) = 3*a(n-1) - a(n-2) - 3*a(n-3) + a(n-4).
a(n+1) = a(n) + A166920(n).
a(n+4) - a(n) = 13, 28, 58, 118, ... = 15*2^n - 2 = A060182(n+2).
With b(n) = 0, 0, 0, A011377(n) = 0, 0, 0, 1, 3, 8, 18, ..., then a(n) = 2*b(n+1) - b(n).
a(n+2) - 2*a(n+1) + a(n) = A014551(n).
G.f.: x^2*(2 - x)/((1-x)^2*(1 - x - 2*x^2)). - Stefano Spezia, Oct 28 2018
a(n) = ((-1)^n + 2^(n+2) - 2*n - 5) / 4. - Colin Barker, Oct 28 2018
Extensions
Three terms corrected by Colin Barker, Oct 28 2018
Comments