A055619 a(n) = A*10^(4*n+1)+B with A=99000*(10^(4*n)-1)/9999+10 and B=9900*(10^(4*n)-1)/9999+1.

9901009901, 990099010099009901, 99009900990100990099009901, 9900990099009901009900990099009901, 990099009900990099010099009900990099009901

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn
• easy

Examples

			a(2) = (99000*(10^8-1)/9999+10)*10^9+9900*(10^8-1)/9999+1 = 990099010099009901.
Note that 990099010099009901 = 990099010^2+099009901^2.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (100010001, -1000100010000, 1000000000000).

Crossrefs

Subsequence of A055616.

Programs

Magma

[(100^(2*n+1)+1)^2/101: n in [1..5]]; // Bruno Berselli, Jul 23 2013

Mathematica

Table[(100^(2 n + 1) + 1)^2/101, {n, 5}] (* Bruno Berselli, Jul 23 2013 *)

PARI

a(n) = (99000*(10^(4*n)-1)/9999+10)*10^(4*n+1)+9900*(10^(4*n)-1)/9999+1 \\ Michel Marcus, Jul 23 2013

Formula

a(n) = ( 100^(2*n+1) + 1 )^2 / 101. [Bruno Berselli, Jul 23 2013]

G.f.: 101*x*(98029801-1000000010000*x+1000000000000*x^2)/((1-x)*(1-10000*x)*(1-100000000*x)). [Bruno Berselli, Jul 23 2013]