

A168230


a(n) = n + 2  a(n1) for n>1; a(1) = 0.


8



0, 4, 1, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 27, 24, 28, 25, 29, 26, 30, 27, 31, 28, 32, 29, 33, 30, 34, 31, 35, 32, 36, 33, 37, 34, 38, 35, 39, 36, 40, 37
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Interleaving of A001477 and A000027 without first three terms.
Binomial transform of 0, 4 followed by a signed version of A005009.
Inverse binomial transform of A034007 without first and third term.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,1).


FORMULA

G.f.: x^2*(4  3*x)/((1+x)*(1x)^2).
a(n) = (7*(1)^n + 2*n + 5)/4.
a(n) = a(n2) + 1 for n>2; a(1)=0, a(2)=4.
a(n+1)  a(n) = A168309(n).
a(n) = a(n1) + a(n2)  a(n3).  Colin Barker, Nov 08 2014
E.g.f.: (1/4)*(7  12*exp(x) + (5 + 2*x)*exp(2*x))*exp(x).  G. C. Greubel, Jul 16 2016


EXAMPLE

a(2) = 2+2a(1) = 40 = 4; a(3) = 3+2a(2) = 54 = 1.


MATHEMATICA

a=3; Table[a=na, {n, 3, 200}] (* Vladimir Joseph Stephan Orlovsky, Nov 22 2009 *)
CoefficientList[Series[x (4  3 x) / ((1 + x) (1  x)^2), {x, 0, 100}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{1, 1, 1}, {0, 4, 1}, 50] (* G. C. Greubel, Jul 16 2016 *)
nxt[{n_, a_}]:={n+1, n+3a}; NestList[nxt, {1, 0}, 80][[All, 2]] (* Harvey P. Dale, May 28 2021 *)


PROG

(MAGMA) [ n eq 1 select 0 else Self(n1)+n+2: n in [1..75] ];
(PARI) Vec(x^2*(43*x)/((1+x)*(1x)^2) + O(x^100)) \\ Colin Barker, Nov 08 2014


CROSSREFS

Cf. A001477 (nonnegative integers), A000027 (positive integers), A168309 (repeat 4,3), A005009 (7*2^n), A034007 (first differences of A045891).
Sequence in context: A131230 A076063 A035590 * A080414 A067061 A115210
Adjacent sequences: A168227 A168228 A168229 * A168231 A168232 A168233


KEYWORD

nonn,easy


AUTHOR

Vincenzo Librandi, Nov 21 2009


EXTENSIONS

Edited, three comments, four formulas, MAGMA program added by Klaus Brockhaus, Nov 22 2009


STATUS

approved



