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, 99009900990099009900990100990099009900990099009901, 9900990099009900990099009901009900990099009900990099009901

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..100

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

Formula

From Bruno Berselli, Jul 23 2013: (Start)

a(n) = (100^(2*n+1) + 1)^2 / 101.

G.f.: 101*x*(98029801-1000000010000*x+1000000000000*x^2)/((1-x)*(1-10000*x)*(1-100000000*x)). (End)

From Elmo R. Oliveira, Jul 09 2026: (Start)

a(n) = 100010001*a(n-1) - 1000100010000*a(n-2) + 1000000000000*a(n-3).

E.g.f.: (1/101)*exp(x)*(1 + 200*exp(9999*x) + 10000*exp(99999999*x)) - 101. (End)

Example

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

Mathematica

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

Prog

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

Crossrefs

Subsequence of A055616.

Sequence in context: A157745 A159473 A174844 * A057072 A130427 A130431

Adjacent sequences: A055616 A055617 A055618 * A055620 A055621 A055622

Keyword

nonn,easy,changed

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Extensions

a(6) onward from Andrew Howroyd, Nov 07 2025

Status

approved