A113225 a(2n) = A011900(n), a(2n+1) = A001109(n+1).

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

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).

For n >= 1, a(n) is also the edge cover number and edge cut count of the n-Pell graph. - Eric W. Weisstein, Aug 01 2023

Also the independence number, Lovasz number, and Shannon capacity of the n-Pell graph. - Eric W. Weisstein, Aug 01 2023

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

References

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

Links

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

Eric Weisstein's World of Mathematics, Edge Cover Number.

Eric Weisstein's World of Mathematics, Edge Cut.

Eric Weisstein's World of Mathematics, Independence Number.

Eric Weisstein's World of Mathematics, Lovasz Number.

Eric Weisstein's World of Mathematics, Pell Graph.

Eric Weisstein's World of Mathematics, Shannon Capacity.

Index entries for linear recurrences with constant coefficients, signature (2,2,-2,-1).

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

a(n) = (1 + (-1)^n + 2 A000129(n+1))/4. - Eric W. Weisstein, Aug 01 2023

a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4). - Eric W. Weisstein, Aug 01 2023

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

Mathematica

Ceiling[Fibonacci[Range[20], 2]/2]
Table[(1 + (-1)^n + 2 Fibonacci[n + 1, 2])/4, {n, 0, 20}] // Expand
CoefficientList[Series[-(-1 + x + x^2)/(1 - 2 x - 2 x^2 + 2 x^3 + x^4), {x, 0, 20}], x]
LinearRecurrence[{2, 2, -2, -1}, {1, 1, 3, 6}, 20]

Prog

(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 * A298539 A209450 A291013

Adjacent sequences: A113222 A113223 A113224 * A113226 A113227 A113228

Keyword

easy,nonn

Author

Creighton Dement, Oct 18 2005

Status

approved