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

0,1

Links

Table of n, a(n) for n=0..19.

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).

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

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 *)

Crossrefs

See A059729 for the actual squares.

Sequence in context: A042533 A355056 A309185 * A371744 A198256 A232972

Adjacent sequences: A169960 A169961 A169962 * A169964 A169965 A169966

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Aug 07 2010

Status

approved