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A192237 a(n) = 2*(a(n-1) + a(n-2) + a(n-3)) - a(n-4) for n >= 4, with initial terms 0,0,0,1. 5
0, 0, 0, 1, 2, 6, 18, 51, 148, 428, 1236, 3573, 10326, 29842, 86246, 249255, 720360, 2081880, 6016744, 17388713, 50254314, 145237662, 419744634, 1213084507, 3505879292, 10132179204, 29282541372, 84628115229, 244579792318, 706848718634, 2042830710990, 5903890328655, 17062559724240, 49311712809136, 142513495013072 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,2,-1).

FORMULA

G.f.: x^3 / (1 - 2*x - 2*x^2 - 2*x^3 + x^4). - Colin Barker, Sep 12 2012 and Sep 06 2018

MATHEMATICA

q[x_]:= x + 1;

reductionRules = {x^y_?EvenQ -> q[x]^(y/2), x^y_?OddQ -> x q[x]^((y - 1)/2)};

t = Table[Last[Most[FixedPointList[Expand[#1 /. reductionRules] &, ChebyshevU[n, x]]]], {n, 1, 40}];

Table[Coefficient[Part[t, n], x, 0], {n, 1, 40}] (* A192235 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 40}] (* A192236 *)

Table[Coefficient[Part[t, n]/2, x, 1], {n, 1, 40}] (* A192237 *)

(* by Peter J. C. Moses, Jun 25 2011 *)

LinearRecurrence[{2, 2, 2, -1}, {0, 0, 0, 1}, 40] (* Vincenzo Librandi, Sep 06 2018 *)

PROG

(PARI) concat(vector(3), Vec(x^3/(1-2*x-2*x^2-2*x^3+x^4) + O(x^40))) \\ Colin Barker, Sep 06 2018

(MAGMA) I:=[0, 0, 0, 1]; [n le 4 select I[n] else 2*(Self(n-1)+Self(n-2) +Self(n-3))-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Sep 06 2018

(Sage) (x^3/(1-2*x-2*x^2-2*x^3+x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jul 30 2019

(GAP) a:=[0, 0, 0, 1];; for n in [5..40] do a[n]:=2*a[n-1]+2*a[n-2]+2*a[n-3] -a[n-4]; od; a; # G. C. Greubel, Jul 30 2019

CROSSREFS

Cf. A192232, A192235.

With a different offset, equals (A192236)/2.

Other sequences with this recurrence but different initial conditions: A192234, A317973, A317974, A317975, A317976.

Sequence in context: A196593 A248735 A219136 * A034525 A018249 A245285

Adjacent sequences:  A192234 A192235 A192236 * A192238 A192239 A192240

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 26 2011

EXTENSIONS

Entry revised (with new offset and initial terms) by N. J. A. Sloane, Sep 03 2018

STATUS

approved

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Last modified July 14 09:17 EDT 2020. Contains 335720 sequences. (Running on oeis4.)