A217446 Sum of the squares of numbers obtained by digit permutations of the concatenation of first n numbers.

1, 585, 331668, 213208980, 156226437720, 129158041750920, 119164964083502400, 121503028361696976960, 135757575541042424323200, 165013333307050666667644800, 216831999996550400000012812800, 306342399999513113600000180544000, 463124479999926454528000002723302400

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Formula

a(n) = (1/12)*(n+1)!*(n*R'(n)+(3*n+2)*R(n)^2) with R(n) = (10^n-1)/9 and R'(n) = (10^(2*n)-1)/99.

Example

a(1) = 1^2 = 1.
a(2) = 12^2 + 21^2 = 585.
a(3) = 123^2 + 132^2 + 213^2 + 231^2 + 312^2 + 321^2 = 331668.

Maple

R:= n-> (10^n-1)/9: RP:= n-> (10^(2*n)-1)/99:
a:= n-> (1/12)*(n+1)!*(n*RP(n)+(3*n+2)*R(n)^2):
seq (a(n), n=1..15);  # Alois P. Heinz, Oct 03 2012

Crossrefs

Cf. A071268.

Sequence in context: A258331 A352979 A022243 * A171436 A020362 A051988

Adjacent sequences: A217443 A217444 A217445 * A217447 A217448 A217449

Keyword

nonn,base

Author

Roger Cuculière, Oct 03 2012

Extensions

More terms from Alois P. Heinz, Oct 03 2012

Status

approved