OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Index entries for linear recurrences with constant coefficients, signature (3,-3,1,2,-6,6,-2,-1,3,-3,1).
FORMULA
G.f.: x * (1 + 2*x + 2*x^2 + 2*x^3 + 10*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + x^8) / ( (1 - x)^3 * (1 - x^4)^2 ).
a(n) = a(-1 - n) for all n in Z. floor( sqrt( a(n))) = A054925(n+1).
EXAMPLE
G.f. = x + 5*x^2 + 14*x^3 + 30*x^4 + 65*x^5 + 125*x^6 + 216*x^7 + ...
MATHEMATICA
CoefficientList[Series[x*(1+2*x+2*x^2+2*x^3+10*x^4+2*x^5+2*x^6+2*x^7+ x^8)/((1-x)^3*(1-x^4)^2), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2018 *)
PROG
(PARI) {a(n) = if( n<0, n = -1-n); polcoeff( x * (1 + 2*x + 2*x^2 + 2*x^3 + 10*x^4 + 2*x^5 + 2*x^6 + 2*x^7 + x^8) / ( (1 - x)^3 * (1 - x^4)^2 ) + x * O(x^n), n)};
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 +2*x+2*x^2+2*x^3+10*x^4+2*x^5+2*x^6+2*x^7+ x^8)/((1-x)^3*(1-x^4)^2))); // G. C. Greubel, Aug 07 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Mar 01 2014
STATUS
approved