A169963 Number of (2n+1)-digit squares in carryless arithmetic mod 10.

5, 46, 452, 4504, 45008, 450016, 4500032, 45000064, 450000128, 4500000256, 45000000512, 450000001024, 4500000002048, 45000000004096, 450000000008192, 4500000000016384, 45000000000032768, 450000000000065536, 4500000000000131072, 45000000000000262144

Offset: 0

Author

N. J. A. Sloane, Aug 07 2010

Keywords

• nonn
• base
• easy

Links

• David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
• Index entries for sequences related to carryless arithmetic
• Index entries for linear recurrences with constant coefficients, signature (12,-20).

Crossrefs

See A059729 for the actual squares.

Programs

Maple

f :- n->2^((n-1)/2) + add( 5^d*2^((n+1)/2),d=0..(n-3)/2) + 2^((n+3)/2)*5^((n-1)/2);

Mathematica

LinearRecurrence[{12, -20}, {5, 46}, 25] (* Paolo Xausa, Jun 26 2024 *)

Formula

For formula see Maple code.

a(n) = 12*a(n-1)-20*a(n-2). G.f.: -(14*x-5) / ((2*x-1)*(10*x-1)). - Colin Barker, May 11 2013