A177423 a(n) = 6*a(n-1)-8*a(n-2)-3 for n > 10; a(0)=753, a(1)=5043, a(2)=25779, a(3)=213003, a(4)=1687623, a(5)=18171219, a(6)=73344977, a(7)=769993485, a(8)=4480470831, a(9)=17582325855, a(10)=69524390079.

753, 5043, 25779, 213003, 1687623, 18171219, 73344977, 769993485, 4480470831, 17582325855, 69524390079, 276487733631, 1102731281151, 4404485817855, 17605064657919, 70394501404671, 281526491164671, 1126002935750655

Offset

0,1

Comments

Related to Reverse and Add trajectory of 442 in base 2: a(n) = A075268(4*n+3)/3, i.e. one third of fourth 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).

Formula

a(n) = 4^(n+8)+12576771*2^(n-4)-1 for n > 8.

G.f.: (753-228*x+1020*x^2+97128*x^3+517164*x^4+9133668*x^5-31930858*x^6 +497474728*x^7-28023638*x^8-3587820988*x^9+3014752848*x^10+125798400*x^11) / ((1-x)*(1-2*x)*(1-4*x)).

G.f. for the sequence starting at a(9): 3*x^9*(5860775285-17850630302*x +11989855016*x^2)/((1-x)*(1-2*x)*(1-4*x)).

Mathematica

CoefficientList[Series[(753 - 228 x + 1020 x^2 + 97128 x^3 + 517164 x^4 + 9133668 x^5 - 31930858 x^6 + 497474728 x^7 - 28023638 x^8 - 3587820988 x^9 + 3014752848 x^10 + 125798400 x^11)/((1 - x) (1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)

Prog

(PARI) {m=18; v=concat([753, 5043, 25779, 213003, 1687623, 18171219, 73344977, 769993485, 4480470831, 17582325855, 69524390079], vector(m-11)); for(n=12, m, v[n]=6*v[n-1]-8*v[n-2]-3); v}
(Magma) [753, 5043, 25779, 213003, 1687623, 18171219, 73344977, 769993485, 4480470831] cat [4^(n+8)+12576771*2^(n-4)-1: n in [9..25]]; // Vincenzo Librandi, Sep 24 2013

Crossrefs

Cf. A075268 (Reverse and Add trajectory of 442 in base 2), A177420, A177421, A177422.

Sequence in context: A332000 A223447 A200211 * A251330 A092449 A197107

Adjacent sequences: A177420 A177421 A177422 * A177424 A177425 A177426

Keyword

nonn,easy

Author

Klaus Brockhaus, May 07 2010

Status

approved