0,1

Sequence generalized : a(n)=a(0)*(B^n) + F(n)* [(B^n)-1]/(B-1); a(0), B integers, F(n) arithmetic function.

Examples:

a(0)=1, B=10, F(n)=1 gives A002275,F(n)=2 gives A090843,F(n)=3 gives A097166,F(n)=4 gives A099914, F(n)=5 gives A099915.

a(0)=1, B=2, F(n)=1 gives A000225,F(n)=2 gives A033484,F(n)=3 gives A036563,F(n)=4 gives A048487, F(n)=5 gives A048488,F(n)=6 gives A048489.

a(0)=1, B=3, F(n)=1 gives A003462,F(n)=2 gives A048473,F(n)=3 gives A134931,F(n)=4 gives A058481, F(n)=5 gives A116952.

a(0)=1, B=4, F(n)=1 gives A002450,F(n)=2 gives A020989,F(n)=3 gives A083420,F(n)=4 gives A083597, F(n)=5 gives A083584.

a(0)=1, B=5, F(n)=1 gives A003463,F(n)=2 gives A057651,F(n)=3 gives A117617,F(n)=4 gives A081655.

a(0)=2, B=10, F(n)=1 gives A037559,F(n)=2 gives A002276.

a(n)=3*(10^n) + (n*n+1)* [(10^n)-1]/9

O.g.f.: -(-3+67*x-478*x^2+1002*x^3-850*x^4+100*x^5)/[(-1+x)^3 *(-1+10*x)^3 ] . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 16 2008

a(3)= 3*10^3 + (3*3+1)*[10^3 -1]/9 =4110

Adjacent sequences: A137212 A137213 A137214 this_sequence A137216 A137217 A137218

Sequence in context: A037799 A091706 A091705 this_sequence A123336 A058479 A129431

easy,nonn

Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Mar 06 2008

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 16 2008