File: recur.dem

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load("recur.mac");
(declare(n, integer),
  matchdeclare(nn, lambda([e], symbolp(e) and featurep(e, integer))),
  tellsimpafter('binomial(nn, nn), 1),
  'done)$

char(u(n+3)+6*u(n+2)+12*u(n+1)+8*u(n),0,u,n,3,[u(0)=1,u(1)=-2,u(2)=8]);
char(u(n+1)-u(n),(1/6)*n*(n-1)*(n-2)+n-1,u,n,1,[u(0)=1]);
char(u(n+2)-2*u(n+1)+u(n),n**2,u,n,2,[u(0)=0,u(1)=1]);
genf(u(n+2)-u(n),2**n,u,n,2,[u(0)=1,u(1)=0]);
char(u(n+2)-4*u(n),3+2*n,u,n,2,[u(0)=1,u(1)=0]);
varc1(u(n+1)-(n+1)*u(n),1,u,n,1,[u(0)=1]);
varc2(u(n+1)-(n+1)*u(n),1,u,n,1,[u(0)=1]);