A096885 Related to diagonals of Pascal's triangle.

1, 100, 10001, 1000200, 100030001, 10004000300, 1000500060001, 100060010000400, 10007001500100001, 1000800210020000500, 100090028003500150001, 10010003600560035000600, 1001100450084007000210001, 100120055012001260056000700, 10013006601650210012600280001, 1001400780220033002520084000800

Offset: 0

Author

Paul Barry, Jul 14 2004

Keywords

• easy
• nonn

Links

• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (100,1).

Crossrefs

Cf. A096884, A007318, A000045.

Formula

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*100^(n-2k).

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 100*a(n-1) + a(n-2), n > 1; a(0)=1, a(1)=100.

G.f.: 1/(1-100*x-x^2). (End)

E.g.f.: exp(50*x)*(cosh(sqrt(2501)*x) + 50*sinh(sqrt(2501)*x)/sqrt(2501)). - Stefano Spezia, Aug 05 2024

Extensions

a(12)-a(15) from Stefano Spezia, Aug 05 2024