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A154348
a(n) = 16*a(n-1) - 56*a(n-2) for n>1, with a(0)=1, a(1)=16.
2
1, 16, 200, 2304, 25664, 281600, 3068416, 33325056, 361369600, 3915710464, 42414669824, 459354931200, 4974457389056, 53867442077696, 583309459456000, 6316374594945024, 68396663789584384, 740629643316428800
OFFSET
0,2
COMMENTS
Third binomial transform of A164609, fourth binomial transform of A164608, fifth binomial transform of A054490, sixth binomial transform of A164607, seventh binomial transform of A083100, eighth binomial transform of A164683.
lim_{n -> infinity} a(n)/a(n-1) = 8 + 2*sqrt(2) = 10.8284271247....
FORMULA
a(n) = 16*a(n-1) - 56*a(n-2) for n>1. - Philippe Deléham, Jan 12 2009
a(n) = ( (8 + 2*sqrt(2))^n - (8 - 2*sqrt(2))^n )/(4*sqrt(2)).
G.f.: 1/(1 - 16*x + 56*x^2). - Klaus Brockhaus, Jan 12 2009; corrected Oct 08 2009
E.g.f.: (1/(2*sqrt(2)))*exp(8*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 13 2016
MATHEMATICA
Join[{a=1, b=16}, Table[c=16*b-56*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
LinearRecurrence[{16, -56}, {1, 16}, 30] (* Harvey P. Dale, Aug 31 2016 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((8+2*r)^n-(8-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009
CROSSREFS
Cf. A002193 (decimal expansion of sqrt(2)), A164609, A164608, A054490, A164607, A083100, A164683.
Sequence in context: A226869 A257289 A125451 * A129333 A001810 A016165
KEYWORD
nonn,easy
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
EXTENSIONS
Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
Offset corrected. - R. J. Mathar, Jun 19 2021
STATUS
approved