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A177683
a(n) = 6*a(n-1)-8*a(n-2) for n > 4; a(0)=191, a(1)=1587, a(2)=14161, a(3)=123004, a(4)=508152.
5
191, 1587, 14161, 123004, 508152, 2064880, 8324064, 33425344, 133959552, 536354560, 2146450944, 8587869184, 34355607552, 137430691840, 549739290624, 2198990209024, 8796026929152, 35184239902720, 140737223983104
OFFSET
0,1
COMMENTS
Related to Reverse and Add trajectory of 537 in base 2: a(n) = A077076(4*n+1)/6, i.e., one sixth of second quadrisection of A077076.
FORMULA
a(n) = 2*4^(n+5)-2017*2^(n-1) for n > 2.
G.f.: (191+441*x+6167*x^2+50734*x^3-116584*x^4) / ((1-2*x)*(1-4*x)).
G.f. for the sequence starting at a(3): 4*x^3*(30751-57468*x) / ((1-2*x)*(1-4*x)).
MATHEMATICA
Join[{191, 1587, 14161}, Transpose[NestList[{Last[#], 6Last[#]-8First[#]}&, {123004, 508152}, 20]][[1]]] (* Harvey P. Dale, Mar 06 2011 *)
CoefficientList[Series[(191 + 441 x + 6167 x^2 + 50734 x^3 - 116584 x^4)/((1 - 2 x) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 24 2013 *)
LinearRecurrence[{6, -8}, {191, 1587, 14161, 123004, 508152}, 20] (* Harvey P. Dale, Oct 16 2019 *)
PROG
(PARI) {m=19; v=concat([191, 1587, 14161, 123004, 508152], vector(m-5)); for(n=6 , m, v[n]=6*v[n-1]-8*v[n-2]); v}
(Magma) [191, 1587, 14161] cat [2*4^(n+5)-2017*2^(n-1): n in [3..25]]; // Vincenzo Librandi, Sep 24 2013
CROSSREFS
Cf. A077076 (Reverse and Add trajectory of 537 in base 2), A177682, A177684, A177685.
Sequence in context: A107955 A264844 A061331 * A209549 A218595 A296580
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, May 12 2010
STATUS
approved