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A113225 a(2n) = A011900(n), a(2n+1) = A001109(n+1). 3
1, 1, 3, 6, 15, 35, 85, 204, 493, 1189, 2871, 6930, 16731, 40391, 97513, 235416, 568345, 1372105, 3312555, 7997214, 19306983, 46611179, 112529341, 271669860, 655869061, 1583407981, 3822685023, 9228778026, 22280241075, 53789260175 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n+1) - a(n) = A097075(n+1), a(n) + a(n+1) = A024537(n+1), a(n+2) - a(n+1) - a(n) = A105635(n+1).

REFERENCES

C. Dement, Floretion Integer Sequences (work in progress).

LINKS

Table of n, a(n) for n=0..29.

FORMULA

G.f.: y/(y^2-1) where y=x/(x^2+x-1) if offset=1. - Michael Somos, Sep 09 2006

G.f.: (-1+x+x^2)/((1-x)*(x+1)*(x^2+2*x-1)).

Diagonal sums of A119468. - Paul Barry, May 21 2006

MAPLE

seq(iquo(fibonacci(n, 2), 1)-iquo(fibonacci(n, 2), 2), n=1..30); # Zerinvary Lajos, Apr 20 2008

with(combinat):seq(ceil(fibonacci(n, 2)/2), n=1..30); # Zerinvary Lajos, Jan 12 2009

PROG

Floretion Algebra Multiplication Program, FAMP Code: -2jbasejseq[B*C], B = - .5'i + .5'j - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'; C = + .5'i + .5i' + .5'ii' + .5e

(PARI) {a(n)=local(y); if(n<0, 0, n++; y=x/(x^2+x-1)+x*O(x^n); polcoeff( y/(y^2-1), n))} /* Michael Somos, Sep 09 2006 */

CROSSREFS

Cf. A113224, A002315, A082639, A100828.

Sequence in context: A024416 A076375 A190586 * A209450 A291013 A017924

Adjacent sequences:  A113222 A113223 A113224 * A113226 A113227 A113228

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Oct 18 2005

STATUS

approved

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Last modified November 23 20:23 EST 2017. Contains 295141 sequences.