A138748 a(n) = (n+(n+1)) + (n*(n+1)) + (n^(n+1)).

1, 6, 19, 100, 1053, 15666, 279991, 5764872, 134217817, 3486784510, 100000000131, 3138428376876, 106993205379253, 3937376385699498, 155568095557812463, 6568408355712890896, 295147905179352826161, 14063084452067724991350, 708235345355337676358011, 37589973457545958193356020, 2097152000000000000000000461

Offset: 0

Author

Anthony J. DeFusco II, Mar 28 2008

Keywords

• easy
• nonn

Comments

Sum of three arithmetic operations (sum, product, powers) of two consecutive integers.

Examples

			a(0) = (0+1) + (0*1) + (0^1) = 1;
a(1) = (1+2) + (1*2) + (1^2) = 6;
a(2) = (2+3) + (2*3) + (2^3) = 19; etc.
		

Programs

Maple

A028387 := proc(n) n+(n+1)^2 ; end: A007778 := proc(n) n^(n+1) ; end: A138748 := proc(n) A028387(n)+A007778(n) ; end: seq(A138748(n),n=0..20) ; # R. J. Mathar, Apr 03 2008

Mathematica

Table[2n+1+n(n+1)+n^(n+1),{n,0,20}] (* Harvey P. Dale, Sep 13 2024 *)

Formula

a(n) = A028387(n) + A007778(n). - R. J. Mathar, Apr 03 2008

Extensions

More terms from R. J. Mathar, Apr 03 2008