

A098181


Odd numbers with two times the positive even numbers repeated in order between them.


4



1, 3, 4, 4, 5, 7, 8, 8, 9, 11, 12, 12, 13, 15, 16, 16, 17, 19, 20, 20, 21, 23, 24, 24, 25, 27, 28, 28, 29, 31, 32, 32, 33, 35, 36, 36, 37, 39, 40, 40, 41, 43, 44, 44, 45, 47, 48, 48, 49, 51, 52, 52, 53, 55, 56, 56, 57, 59, 60, 60, 61, 63, 64, 64, 65, 67, 68, 68, 69, 71, 72, 72
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OFFSET

0,2


COMMENTS

Essentially partial sums of A007877.


LINKS

Table of n, a(n) for n=0..71.
Index to sequences with linear recurrences with constant coefficients, signature (2,2,2,1).


FORMULA

G.f. : (1+x)/((1x)^2(1+x^2)); a(n)=(2n+3)/2cos(pi*n/2)/2+sin(pi*n/2)/2; a(n)=2a(n1)2a(n2)+2a(n3)a(n4).
a(n)=floor(C(n+3, 2)/2)floor(C(n+1, 2)/2)  Paul Barry, Jan 01 2005
a(4n)=4n+1, a(4n+1)=4n+3, a(4n+2)=4n+4, a(4n+3)=4n+4 .  Philippe Deléham, Apr 06 2007
Euler transform of length 4 sequence [ 3, 2, 0, 1].  Michael Somos, Sep 11 2014
a(3n) = a(n) for all n in Z.  Michael Somos, Sep 11 2014


EXAMPLE

G.f. = 1 + 3*x + 4*x^2 + 4*x^3 + 5*x^4 + 7*x^5 + 8*x^6 + 8*x^7 + 9*x^8 + ...


PROG

(PARI) {a(n) = n\4*4 + [1, 3, 4, 4][n%4+1]}; /* Michael Somos, Sep 11 2014 */


CROSSREFS

Cf. A098180.
Sequence in context: A113454 A157726 A082223 * A111914 A051665 A028263
Adjacent sequences: A098178 A098179 A098180 * A098182 A098183 A098184


KEYWORD

easy,nonn,changed


AUTHOR

Paul Barry, Aug 30 2004


STATUS

approved



