A257487 Expansion of ( -4+15*x-8*x^2 ) / ( (x-1)*(x^2-4*x+1) ).

4, 5, 13, 44, 160, 593, 2209, 8240, 30748, 114749, 428245, 1598228, 5964664, 22260425, 83077033, 310047704, 1157113780, 4318407413, 16116515869, 60147656060, 224474108368, 837748777409, 3126521001265, 11668335227648, 43546819909324

Offset: 0

Author

R. J. Mathar, Apr 26 2015

Keywords

• nonn
• easy

Links

• M. Knor, R. Skrekovski, Wiener index of generalized 4-stars and their quadratic line graphs, Austral. J. Combinat. 58 (1) (2014) 119-126, eq. (11).
• Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

Crossrefs

Cf. A055845 (first differences).

Programs

Maple

A257487 := proc(n)
    (5+sqrt(3))/4*(2-sqrt(3))^n+(5-sqrt(3))/4*(2+sqrt(3))^n+3/2 ;
    expand(%) ;
end proc:
seq(A257487(n),n=0..30) ;

Mathematica

CoefficientList[Series[(-4+15x-8x^2)/((x-1)(x^2-4x+1)),{x,0,30}],x] (* or *) LinearRecurrence[{5,-5,1},{4,5,13},30] (* Harvey P. Dale, Dec 29 2024 *)

PARI

Vec(( -4+15*x-8*x^2 ) / ( (x-1)*(x^2-4*x+1) ) + O(x^50)) \\ Michel Marcus, Apr 26 2015

Formula

a(n) = (5*A001353(n+1)-13*A001353(n)+3)/2. - R. J. Mathar, May 26 2016