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

0,2

Links

Table of n, a(n) for n=0..15.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (100,1).

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

Crossrefs

Cf. A096884, A007318, A000045.

Sequence in context: A029801 A098608 A045799 * A267449 A266752 A267523

Adjacent sequences: A096882 A096883 A096884 * A096886 A096887 A096888

Keyword

easy,nonn

Author

Paul Barry, Jul 14 2004

Extensions

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

Status

approved