A177843 a(n) = 6*a(n-1)-8*a(n-2)-9 for n > 3; a(0)=775, a(1)=8919, a(2)=49581, a(3)=197469.

775, 8919, 49581, 197469, 788157, 3149181, 12589821, 50345469, 201354237, 805361661, 3221336061, 12885123069, 51540049917, 206159314941, 824635490301, 3298538422269, 13194146611197, 52776572289021, 211106260844541

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), i.e. first 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), A177844, A177845, A177846.

Programs

Magma

[775, 8919] cat [3*4^(n+5)+27*2^(n+2)-3: n in [2..25]]; // Vincenzo Librandi, Sep 24 2013

Mathematica

CoefficientList[Series[(775 + 3494 x - 2002 x^2 - 30932 x^3 + 28656 x^4)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{7,-14,8},{775,8919,49581,197469,788157},20] (* Harvey P. Dale, Aug 03 2023 *)

PARI

{m=19; v=concat([775, 8919, 49581, 197469], vector(m-4)); for(n=5, m, v[n]=6*v[n-1]-8*v[n-2]-9); v}

Formula

a(n) = 3*4^(n+5)+27*2^(n+2)-3 for n > 1.

G.f.: (775+3494*x-2002*x^2-30932*x^3+28656*x^4) / ((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(2): 9*x^2*(5509-16622*x+11112*x^2) / ((1-x)*(1-2*x)*(1-4*x)).