A097659 a(n) = 1001^n.

1, 1001, 1002001, 1003003001, 1004006004001, 1005010010005001, 1006015020015006001, 1007021035035021007001, 1008028056070056028008001, 1009036084126126084036009001, 1010045120210252210120045010001, 1011055165330462462330165055011001, 1012066220495792924792495220066012001

Offset: 0

Author

Reinhard Zumkeller, Aug 18 2004

Keywords

• nonn
• easy

Comments

694 is the smallest exponent e such that 1001^e begins with a digit greater than 1: A000030(a(694)) = 2, A000030(a(693)) = 1. - Reinhard Zumkeller, Nov 05 2010

a(n) gives the n-th row of Pascal's triangle (A007318) as long as all the binomial coefficients have at most three digits, otherwise the binomial coefficients with more than three digits overlap. - Daniel Forgues, Aug 12 2012

References

• Rozsa Peter, Playing with Infinity, New York, Dover Publications, 1957.

Links

• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (1001).

Crossrefs

Cf. A001020, A007318, A096884, A097660.

Programs

PARI

1001^n \\ Charles R Greathouse IV, Jan 30 2012

PARI

my(x='x+O('x^13)); Vec(-1/(1001*x-1)) \\ Elmo R. Oliveira, Jul 06 2025

Formula

From Philippe Deléham, Nov 30 2008: (Start)

a(n) = 1001*a(n-1), n > 0; a(0)=1.

G.f.: 1/(1-1001*x). (End)

From Elmo R. Oliveira, Jul 06 2025: (Start)

E.g.f.: exp(1001*x).

a(n) = 91^n * A001020(n). (End)

Extensions

More terms from Elmo R. Oliveira, Jul 06 2025