A176632 a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 2; a(0) = 77, a(1) = 897, a(2) = 3333.

77, 897, 3333, 12813, 50205, 198717, 790653, 3154173, 12599805, 50365437, 201394173, 805441533, 3221495805, 12885442557, 51540688893, 206160592893, 824638046205, 3298543534077, 13194156834813, 52776592736253

Offset: 0

Author

Klaus Brockhaus, Apr 22 2010

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 77 in base 2: a(n) = A075253(4*n), i.e., first quadrisection of A075253.

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. A075253 (Reverse and Add trajectory of 77 in base 2), A176633, A176634, A176635, A171471.

Programs

Magma

[77] cat [3*(64*4^n+22*2^n-1): n in [1..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(77 + 358 x - 1868 x^2 + 1424 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
Join[{77},RecurrenceTable[{a[1]==897,a[2]==3333,a[n]==6a[n-1]-8a[n-2]- 9},a[n],{n,20}]] (* Harvey P. Dale, May 21 2019 *)

PARI

{m=20; v=concat([77, 897, 3333], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}

Formula

a(n) = 3*(64*4^n+22*2^n-1) for n > 0, a(0) = 77.

G.f.: (77+358*x-1868*x^2+1424*x^3)/((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(1): 3*x*(299-982*x+680*x^2)/((1-x)* (1-2*x)*(1-4*x)).