A177421 a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 10; a(0)=629, a(1)=6585, a(2)=26259, a(3)=221931, a(4)=1917027, a(5)=18285939, a(6)=125792217, a(7)=703932681, a(8)=7131271077, a(9)=26172260445, a(10)=103884128445.

629, 6585, 26259, 221931, 1917027, 18285939, 125792217, 703932681, 7131271077, 26172260445, 103884128445, 413926687101, 1652487095037, 6603509073405, 26401157680125, 105578873493501, 422263979519997, 1688952889171965

Offset: 0

Author

Klaus Brockhaus, May 07 2010

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n+1), i.e. second quadrisection of A075268.

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. A075268 (Reverse and Add trajectory of 442 in base 2), A177420, A177422, A177423.

Programs

Magma

[629, 6585, 26259, 221931, 1917027, 18285939, 125792217, 703932681, 7131271077] cat [6*4^(n+7)[phone]*2^(n-4)-3: n in [9..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(629 + 2182 x - 11030 x^2 + 125276 x^3 + 678456 x^4 + 7763712 x^5 + 22853574 x^6 + 64054092 x^7 + 3818545836 x^8 - 14897917296 x^9 + 14884638960 x^10 - 3900734400 x^11)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)

PARI

{m=18; v=concat([629, 6585, 26259, 221931, 1917027, 18285939, 125792217, 703932681, 7131271077, 26172260445, 103884128445], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}

Formula

a(n) = 6*4^(n+7)[phone]*2^(n-4)-3 for n > 8.

G.f.: (629+2182*x-11030*x^2+125276*x^3+678456*x^4+7763712*x^5+22853574*x^6 [phone]*x^7+3818545836*x^8-14897917296*x^9+14884638960*x^10-3900734400*x^11) / ((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(9): 3*x^9*(8724086815-26440564890*x+17716478072*x^2) / ((1-x)*(1-2*x)*(1-4*x)).