A135574 - OEIS

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

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OFFSET

0,3

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).

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

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

MATHEMATICA

LinearRecurrence[{0, 3, 0, 3, 0, 4}, {0, 0, 3, 1, 11, 6}, 41] (* G. C. Greubel, Oct 19 2016 *)

PROG

(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

(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

CROSSREFS

Cf. A010892, A024495, A135575.

Sequence in context: A110165 A111965 A110440 * A008969 A199577 A228534

Adjacent sequences: A135571 A135572 A135573 * A135575 A135576 A135577

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Feb 24 2008

EXTENSIONS

More terms from R. J. Mathar, Mar 31 2008

More terms from R. J. Mathar, Feb 07 2009

STATUS

approved