A135574 A024495 but with terms swapped in pairs.
0, 0, 3, 1, 11, 6, 42, 21, 171, 85, 683, 342, 2730, 1365, 10923, 5461, 43691, 21846, 174762, 87381, 699051, 349525, 2796203, 1398102, 11184810, 5592405, 44739243, 22369621, 178956971, 89478486, 715827882, 357913941, 2863311531, 1431655765
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,3,0,4).
Programs
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Magma
I:=[0,0,3,1,11,6]; [n le 6 select I[n] else 3*Self(n-2) +3*Self(n-4) +4*Self(n-6): n in [1..41]]; // G. C. Greubel, Jan 05 2022
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Maple
A024495 := proc(n) option remember ; if n <=1 then 0; elif n = 2 then 1; else 3*procname(n-1)-3*procname(n-2)+2*procname(n-3) ; fi; end: A135574 := proc(n) option remember ; if n mod 2 = 0 then A024495(n+1) ; else A024495(n-1) ; fi; end: seq(A135574(n),n=0..40) ; # R. J. Mathar, Feb 07 2009
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Mathematica
LinearRecurrence[{0,3,0,3,0,4},{0,0,3,1,11,6},41] (* G. C. Greubel, Oct 19 2016 *) -
Sage
[(1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*chebyshev_U(n, 1/2) - (1-3*(-1)^n)*chebyshev_U(n-1, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 05 2022
Formula
a(n+1) - 2*a(n) = A135575(n).
O.g.f.: x^2*(3 + x +2*x^2 +3*x^3)/((1-2*x)*(1+2*x)*(x^2-x+1)*(x^2+x+1)). - R. J. Mathar, Mar 31 2008
a(n) = 3*a(n-2) + 3*a(n-4) + 4*a(n-6). - G. C. Greubel, Oct 19 2016
a(n) = (1/6)*(2^(n-1)*(5+3*(-1)^n) - (1+3*(-1)^n)*ChebyshevU(n, 1/2) - (1-3*(-1)^n)*ChebyshevU(n-1, 1/2)). - G. C. Greubel, Jan 05 2022
Extensions
More terms from R. J. Mathar, Mar 31 2008
More terms from R. J. Mathar, Feb 07 2009