The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A093122 a(n) = Jacobsthal(n) * Fibonacci(n+1). 1
 0, 1, 2, 9, 25, 88, 273, 903, 2890, 9405, 30349, 98352, 318045, 1029587, 3331210, 10781001, 34886465, 112897544, 365339961, 1182271695, 3825900650, 12380892261, 40065380357, 129654340704, 419570185125, 1357757761723 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Form a graph from a triangle and its midpoint triangle. This sequence counts walks of length n between two vertices of the midpoint triangle in this configuration. LINKS Table of n, a(n) for n=0..25. Index entries for linear recurrences with constant coefficients, signature (1,7,2,-4). FORMULA G.f.: x*(1+x)/((1+x-x^2)*(1-2*x-4*x^2)); a(n) = A001045(n) * A000045(n+1); a(n) = (2^n/3-(-1)^n/3)*(((1+sqrt(5))/2)^(n+1)/sqrt(5)-((1-sqrt(5))/2)^(n+1)/sqrt(5)). a(n) = a(n-1) + 7*a(n-2) + 2*a(n-3) - 4*a(n-4). - Wesley Ivan Hurt, Sep 04 2022 MATHEMATICA CoefficientList[Series[x*(1 + x)/((1 + x - x^2)*(1 - 2*x - 4*x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 04 2022 *) CROSSREFS Cf. A000045, A001045. Sequence in context: A116454 A295143 A124633 * A305351 A101051 A356401 Adjacent sequences: A093119 A093120 A093121 * A093123 A093124 A093125 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 22 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 10:45 EDT 2024. Contains 372788 sequences. (Running on oeis4.)