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A098586 a(n) = (1/2) * (5*P(n+1) + P(n) - 1), where P(k) are the Pell numbers A000129. 5
2, 5, 13, 32, 78, 189, 457, 1104, 2666, 6437, 15541, 37520, 90582, 218685, 527953, 1274592, 3077138, 7428869, 17934877, 43298624, 104532126, 252362877, 609257881, 1470878640, 3551015162, 8572908965, 20696833093, 49966575152, 120629983398, 291226541949 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Hermann Stamm-Wilbrandt, 4 interlaced bisections
FORMULA
a(n) = 3*a(n-1) - a(n-2) - a(n-3) with a(0)=2, a(1)=5, a(2)=13. - Hermann Stamm-Wilbrandt, Aug 26 2014
G.f.: (2-x)/((1-x)*(1-2*x-x^2)). - Robert Israel, Aug 26 2014
a(n) = 7*a(n-2) - 7*a(n-4) + a(n-6), for n>5. - Hermann Stamm-Wilbrandt, Aug 27 2014
a(2*n-1) = A006451(2*n), for n>0. - Hermann Stamm-Wilbrandt, Aug 27 2014
a(2*n) = A124124(2*n+2). - Hermann Stamm-Wilbrandt, Aug 27 2014
a(n) = (-2+(5-3*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(5+3*sqrt(2)))/4. - Colin Barker, Mar 16 2016
MAPLE
A:= LREtools[REtoproc](a(n) = 3*a(n-1) - a(n-2) - a(n-3), a(n), {a(0)=2, a(1)=5, a(2)=13}):
seq(A(n), n=0..100); # Robert Israel, Aug 26 2014
MATHEMATICA
LinearRecurrence[{3, -1, -1}, {2, 5, 13}, 28] (* Hermann Stamm-Wilbrandt, Aug 26 2014 *)
CoefficientList[Series[(2-x)/((1-x)*(1-2*x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 03 2018
PROG
(PARI) Vec((2-x)/((1-x)*(1-2*x-x^2)) + O(x^50)) \\ Colin Barker, Mar 16 2016
(Magma) I:=[2, 5, 13]; [n le 3 select I[n] else 3*Self(n-1) - Self(n-2) - Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 03 2018
CROSSREFS
Sequence in context: A116702 A098156 A267862 * A199812 A255170 A255630
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Oct 03 2004
EXTENSIONS
Formula supplied by Thomas Baruchel, Oct 03 2004
More terms from Emeric Deutsch, Nov 17 2004
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)