

A238315


An oscillating sequence: a(n) = n^2 + 2^(n1)  2*a(n1), n>0, with a(1) = 1.


2



1, 4, 5, 14, 13, 42, 29, 134, 69, 474, 197, 1798, 669, 7050, 2509, 28006, 9813, 111770, 38965, 446758, 155501, 1786634, 621565, 7146054, 2485733, 28583642, 9942309, 114333894, 39768509, 457334794, 159073197, 1829338278
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OFFSET

1,2


COMMENTS

For large n: a(2n)/a(2n1) > 23/2; a(2n+1)/a(2n) > 8/23.
Related oscillating sequences can be formed by changing the offset of the exponent in the second term on the righthand side of the definition (i.e., the power of 2) from (n1) to n, (n+1), (n+2,) etc. In all such cases the values of a(2n1) stays constant: 1, 5, 13, 29, 69, 197, 669, ... which is also given as A239367.
For large n, this and the related sequences all obey a(n)/a(n2) > 4, as the second term is dominant.


LINKS



FORMULA

G.f.: x*(2*x^46*x^3+8*x^2x1) / ((x1)^3*(2*x1)*(2*x+1)).  Colin Barker, Mar 31 2014


PROG

(PARI) Vec(x*(2*x^46*x^3+8*x^2x1)/((x1)^3*(2*x1)*(2*x+1)) + O(x^100)) \\ Colin Barker, Mar 31 2014


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



