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A163114 a(n) = 5*a(n-2) for n > 2; a(1) = 3, a(2) = 5. 5
3, 5, 15, 25, 75, 125, 375, 625, 1875, 3125, 9375, 15625, 46875, 78125, 234375, 390625, 1171875, 1953125, 5859375, 9765625, 29296875, 48828125, 146484375, 244140625, 732421875, 1220703125, 3662109375, 6103515625, 18310546875 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Binomial transform is A163062, second binomial transform is A163063, third binomial transform is A098648 without initial 1, fourth binomial transform is A163064, fifth binomial transform is A163065.
LINKS
FORMULA
a(n) = (2-(-1)^n)*5^(1/4*(2*n-1+(-1)^n)).
G.f.: x*(3+5*x)/(1-5*x^2).
a(n) = A056487(n), n>=1.
E.g.f.: cosh(sqrt(5)*x) + 3*sinh(sqrt(5)*x)/sqrt(5) - 1. - Stefano Spezia, Nov 19 2023
MATHEMATICA
CoefficientList[Series[x*(3 + 5*x)/(1 - 5*x^2), {x, 0, 50}], x] (* G. C. Greubel, Dec 21 2017 *)
LinearRecurrence[{0, 5}, {3, 5}, 30] (* Harvey P. Dale, Aug 01 2021 *)
PROG
(Magma) [ n le 2 select 2*n+1 else 5*Self(n-2): n in [1..29] ];
(PARI) x='x+O('x^30); Vec(x*(3+5*x)/(1-5*x^2)) \\ G. C. Greubel, Dec 21 2017
CROSSREFS
Sequence in context: A018272 A328834 A018421 * A111386 A056487 A146582
KEYWORD
nonn,easy
AUTHOR
Klaus Brockhaus, Jul 21 2009
STATUS
approved

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Last modified July 23 13:44 EDT 2024. Contains 374549 sequences. (Running on oeis4.)