A177845 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 2; a(0)=775, a(1)=8919, a(2)=34223.

775, 8919, 34223, 133983, 530111, 2108799, 8411903, 33601023, 134310911, 537057279, 2147856383, 8590680063, 34361229311, 137441935359, 549761777663, 2199035183103, 8796116877311, 35184419799039, 140737583775743

Offset: 0

Author

Klaus Brockhaus, May 14 2010

Keywords

• nonn
• easy

Comments

Related to Reverse and Add trajectory of 775 in base 2: a(n) = A077077(4*n+2)/3, i.e. one third of third quadrisection of A077077.

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. A077077 (Reverse and Add trajectory of 775 in base 2), A177843, A177844, A177846.

Programs

Magma

[775] cat [2*4^(n+5)+91*2^(n+2)-1: n in [1..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

nxt[{a_,b_}]:={b,6b-8a-3}; Join[{775},Transpose[NestList[nxt,{8919,34223},20]][[1]]] (* or *) Join[{775},LinearRecurrence[{7,-14,8},{8919,34223,133983},20]] (* Harvey P. Dale, Mar 04 2013 *)
CoefficientList[Series[(775 + 3494 x - 17360 x^2 + 13088 x^3)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)

PARI

{m=19; v=concat([775, 8919, 34223], vector(m-3)); for(n=4, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}

Formula

a(n) = 2*4^(n+5)+91*2^(n+2)-1 for n > 0.

G.f.: (775+3494*x-17360*x^2+13088*x^3) / ((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(1): x*(8919-28210*x+19288*x^2) / ((1-x)*(1-2*x)*(1-4*x)).

a(0)=775, a(1)=8919, a(2)=34223, a(3)=133983, a(n)=7*a(n-1)-14*a(n-2)+8*a(n-3). - Harvey P. Dale, Mar 04 2013