OFFSET
0,5
COMMENTS
This is a divisibility sequence; that is, if n divides m, then a(n) divides a(m).
REFERENCES
J. A. Sjogren, Cycles and spanning trees. Math. Comput. Modelling 15, No.9, 87-102 (1991).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
J. A. Sjogren, Cycles and Spanning Trees, see equation (3.5)
Index entries for linear recurrences with constant coefficients, signature (0,2,0,2,0,2,0,-1).
FORMULA
EXAMPLE
G.f. = x + x^2 + x^3 + 2*x^4 + 5*x^5 + 5*x^6 + 13*x^7 + 16*x^8 + 37*x^9 + ...
MATHEMATICA
CoefficientList[Series[x*(1+x)*(1-x^2)*(1+x^3)/(1-2*x^2-2*x^4-2*x^6+x^8 ), {x, 0, 50}], x] (* G. C. Greubel, Aug 12 2018 *)
PROG
(PARI) {a(n) = my(m = abs(n)); polcoeff( x * (1 + x) * (1 - x^2) * (1 + x^3) / (1 - 2*x^2 - 2*x^4 - 2*x^6 + x^8) + x * O(x^m), m)};
(PARI) {a(n) = my(m = abs(n), v); v = polroots( Pol([ 1, 2, 4, 2, 1])); sqrtint( round( prod( k=1, 4, v[k]^m - 1, 2^(m%2) / 20)))};
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(x*(1+x)*(1-x^2)*(1+x^3)/(1-2*x^2-2*x^4-2*x^6+x^8 ))); // G. C. Greubel, Aug 12 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Feb 10 2012
STATUS
approved