The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A308244 Triangle T(n,k) read by rows, giving even-numbered coefficients of the matching polynomial of the n-ladder graph. 1
 1, -1, 1, 2, -4, 1, -3, 11, -7, 1, 5, -26, 29, -10, 1, -8, 56, -94, 56, -13, 1, 13, -114, 263, -234, 92, -16, 1, -21, 223, -667, 815, -473, 137, -19, 1, 34, -424, 1577, -2504, 1982, -838, 191, -22, 1, -55, 789, -3538, 7018, -7191, 4115, -1356, 254, -25, 1, 89, -1444, 7622, -18336, 23431, -17266 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS For 0 <= k <= n, T(n,k) is the coefficient of x^(2*k) in the matching polynomial of the n-ladder graph. We take T(0,0)=1. LINKS Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened) Wolfram MathWorld, Ladder Graph Wolfram MathWorld, Matching Polynomial FORMULA Generating function as triangle: (1+x)/(1+2*x-x*y+x^2*y-x^3). T(n,k) = T(n-1,k-1)-2*T(n-1,k)-T(n-2,k-1)+T(n-3,k) for n >= 3 (taking T(n,k)=0 unless 0 <= k <= n). T(n,0) = (-1)^n*A000045(n+1). T(n,1) = (-1)^(n+1)*A002940(n) for n >= 1. T(n,2) = (-1)^n*A002941(n-1) for n >= 2. EXAMPLE Triangle begins 1 -1 1 2 -4 1 -3 11 -7 1 5 -26 29 -10 1 -8 56 -94 56 -13 1 13 -114 263 -234 92 -16 1 -21 223 -667 815 -473 137 -19 1 34 -424 1577 -2504 1982 -838 191 -22 1 MAPLE g:= gfun:-rectoproc({a(n+3)+(-x^2+2)*a(n+2)+x^2*a(n+1)-a(n), a(0)=1, a(1)=x^2-1, a(2)=x^4-4*x^2+2}, a(n), remember): for nn from 0 to 10 do seq(coeff(g(nn), x, k), k=0..2*nn, 2) od; CROSSREFS Cf. A000045, A002940, A002941. Sequence in context: A004515 A258219 A036560 * A117297 A112973 A162303 Adjacent sequences: A308241 A308242 A308243 * A308245 A308246 A308247 KEYWORD sign,tabl AUTHOR Robert Israel, May 16 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 5 05:37 EST 2023. Contains 367575 sequences. (Running on oeis4.)