A108487 Sum binomial(2n-2k,2k)10^(n-k), k=0..floor(n/2).

1, 10, 110, 1600, 25100, 395000, 6201000, 97280000, 1526010000, 23938500000, 375525100000, 5890896000000, 92411011000000, 1449659710000000, 22740940010000000, 356739136000000000, 5596198360100000000

Offset

0,2

Comments

In general, sum{k=0..floor(n/2), C(2n-2k,2k)a^k*b^(n-k)} has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (20,-80,200,-100).

Formula

G.f.: (1-10x-10x^2)/(1-20x-80x^2-200x^3+100x^4); a(n)=20a(n-1)+80a(n-2)+200a(n-3)-100a(n-4).

Mathematica

Table[Sum[Binomial[2n-2k, 2k]10^(n-k), {k, 0, Floor[n/2]}], {n, 0, 30}] (* or *) LinearRecurrence[{20, -80, 200, -100}, {1, 10, 110, 1600}, 30] (* Harvey P. Dale, Mar 20 2023 *)

Crossrefs

Sequence in context: A276507 A049398 A055530 * A099883 A337351 A146753

Adjacent sequences: A108484 A108485 A108486 * A108488 A108489 A108490

Keyword

easy,nonn

Author

Paul Barry, Jun 04 2005

Status

approved