A224521 Numbers a(n) with property a(n) + a(n+5) = 2^(n+5) - 1 = A000225(n+5).
0, 1, 3, 7, 15, 31, 62, 124, 248, 496, 992, 1985, 3971, 7943, 15887, 31775, 63550, 127100, 254200, 508400, 1016800, 2033601, 4067203, 8134407, 16268815, 32537631, 65075262, 130150524, 260301048, 520602096, 1041204192, 2082408385, 4164816771, 8329633543
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,-1,3,-2).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x/((1-x)*(1-2*x)*(1+x^5)) )); // G. C. Greubel, Jun 06 2019 -
Mathematica
CoefficientList[Series[x/((1-x)*(1-2*x)*(1+x^5)), {x,0,40}], x] (* G. C. Greubel, Oct 11 2017 *) LinearRecurrence[{3,-2,0,0,-1,3,-2},{0,1,3,7,15,31,62},40] (* Harvey P. Dale, Apr 29 2020 *) -
PARI
my(x='x+O('x^40)); concat([0], Vec(x/((1-x)*(1-2*x)*(1+x^5)))) \\ G. C. Greubel, Oct 11 2017 -
Python
print([2**(n+5)//33 for n in range(31)]) # Karl V. Keller, Jr., Jul 03 2021
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Sage
(x/((1-x)*(1-2*x)*(1+x^5))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 06 2019
Formula
a(n) + a(n+5) = 2^(n+5) - 1.
From Joerg Arndt, Apr 09 2013: (Start)
G.f.: x/((1-x)*(1+x)*(1-2*x)*(1-x+x^2-x^3+x^4)).
a(n) = +3*a(n-1) -2*a(n-2) -1*a(n-5) +3*a(n-6) -2*a(n-7). (End)
a(n) = floor(2^(n+5)/33). - Karl V. Keller, Jr., Jul 03 2021
Comments