A177682 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 4; a(0)=179, a(1)=1571, a(2)=12511, a(3)=155403, a(4)=572951.

179, 1571, 12511, 155403, 572951, 2194479, 8583263, 33943743, 134996351, 538428159, 2150598143, 8596163583, 34372196351, 137463869439, 549805645823, 2199122919423, 8796292349951, 35184770744319, 140738285666303

Offset: 0

Author

Klaus Brockhaus, May 12 2010

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n)/3, i.e. one third of first quadrisection of A077076.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177683, A177684, A177685.

Programs

Magma

[179, 1571, 12511] cat [2*4^(n+5)+6083*2^(n-1)-1: n in [3..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

Join[{179,1571,12511},LinearRecurrence[{7,-14,8},{155403,572951,2194479},20]] (* Harvey P. Dale, Oct 06 2011 *)
CoefficientList[Series[(179 + 318 x + 4020 x^2 + 88388 x^3 - 352284 x^4 + 259376 x^5)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)

PARI

{m=19; v=concat([179, 1571, 12511, 155403, 572951], vector(m-5)); for(n=6 ,m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

Formula

a(n) = 2*4^(n+5)+6083*2^(n-1)-1 for n > 2.

G.f.: (179+318*x+4020*x^2+88388*x^3-352284*x^4+259376*x^5) / ((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(3): x^3*(155403-514870*x+359464*x^2) / ((1-x)*(1-2*x)*(1-4*x)).