A105867 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A105867

A generalized Chebyshev transform of the Jacobsthal numbers.

0, 1, 1, 7, 11, 47, 95, 327, 759, 2343, 5863, 17095, 44551, 126023, 335687, 934343, 2518215, 6948807, 18846663, 51765703, 140875207, 385980871, 1052314055, 2879386055, 7857807815, 21485572551, 58664391111, 160344666567

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

Apply the Riordan array (1/(1-2x^2),x/(1-2x^2)) to A001045.

LINKS

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (1,6,-2,-4).

FORMULA

G.f.: x/(1-x-6x^2+2x^3+4x^4); a(n)=sum{k=0..floor(n/2), 2^k*C(n-k, k)*A001045(n-2k)}; a(n)=sqrt(3)(sqrt(3)+1)^(n+1)/18+sqrt(3)(sqrt(3)-1)^(n+1)(-1)^n/18-2^(n+1)(-1)^n/9-1/9.

CROSSREFS

Sequence in context: A062209 A086828 A117392 * A166653 A057290 A003599

Adjacent sequences: A105864 A105865 A105866 * A105868 A105869 A105870

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 23 2005

STATUS

approved