OFFSET
0,3
COMMENTS
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
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
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Oct 18 2005
STATUS
approved