A029153 Expansion of 1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)).

1, 0, 1, 1, 1, 1, 3, 1, 3, 3, 4, 3, 7, 4, 7, 7, 9, 7, 13, 9, 14, 13, 17, 14, 22, 17, 24, 22, 28, 24, 35, 28, 38, 35, 43, 38, 52, 43, 56, 52, 63, 56, 74, 63, 79, 74, 88, 79, 101, 88, 108, 101, 119, 108, 134, 119, 143, 134, 156, 143, 174, 156, 185, 174, 200, 185, 221, 200

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

A two-way infinite sequences which is palindromic (up to sign). - Michael Somos, Mar 21 2003

Links

• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 0, -1, 1, 0, -1, -1, 1, 1, -1, -1, 0, 1, -1, 0, 1, 1, 0, -1).

Crossrefs

Cf. A028242, A051263.

Programs

Maple

M := Matrix(21, (i,j)-> if (i=j-1) or (j=1 and member(i, [2, 3, 6, 10, 11, 15, 18, 19])) then 1 elif j=1 and member(i, [5, 8, 9, 12, 13, 16, 21]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..67); # Alois P. Heinz, Jul 25 2008

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)),{x,0,80}],x] (* or *) LinearRecurrence[{0,1,1,0,-1,1,0,-1,-1,1,1,-1,-1,0,1,-1,0,1,1,0,-1},{1,0,1,1,1,1,3,1,3,3,4,3,7,4,7,7,9,7,13,9,14},80] (* Harvey P. Dale, Aug 07 2015 *)

PARI

a(n)=if(n<-20,-a(-21-n),if(n<0,0,polcoeff(1/((1-x^2)*(1-x^3)*(1-x^6)*(1-x^10))+x*O(x^n),n)))

Formula

G.f.: 1/((1-x^2)(1-x^3)(1-x^6)(1-x^10)).

a(n) = A051263(floor(n/2) - n mod 2) = A051263(A028242(n-2)).

a(-21 - n) = -a(n).

a(n) = a(n-2) + a(n-3) - a(n-5) + a(n-6) - a(n-8) - a(n-9) + a(n-10) + a(n-11) - a(n-12) - a(n-13) + a(n-15) - a(n-16) + a(n-18) + a(n-19) - a(n-21).