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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A038737 T(n,n-2), array T as in A038792. 1
1, 6, 23, 73, 211, 581, 1560, 4135, 10890, 28590, 74946, 196326, 514123, 1346148, 3524441, 9227311, 24157645, 63245795, 165579930, 433494205, 1134902916, 2971214796, 7778741748, 20365010748, 53316290821, 139583862066 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,2
COMMENTS
Fifth diagonal of array defined by T(i, 1)=T(1, j)=1, T(i, j)=Max(T(i-1, j)+T(i-1, j-1); T(i-1, j-1)+T(i, j-1)). - Benoit Cloitre, Aug 05 2003
LINKS
FORMULA
G.f.: x^2/((1-3*x+x^2)*(1-x)^3).
a(n) = Sum_{k=0..n} binomial(n+2,k+3)*Fibonacci(k). - Vladimir Kruchinin, Oct 24 2016
a(n) = Sum_{k=0..n} binomial(k+1,2)*Fibonacci(2*n-2*k). - Greg Dresden and Yu Xiao, Jul 19 2020
MATHEMATICA
Rest[Rest[CoefficientList[Series[x^2/((1-3*x+x^2)*(1-x)^3), {x, 0, 27}], x]]] (* Georg Fischer, Apr 15 2020 *)
PROG
(Maxima) a(n):=sum(binomial(n+2, k+3)*fib(k), k, 0, n); /* Vladimir Kruchinin, Oct 24 2016 */
(Sage) [sum(binomial(k+1, 2)*fibonacci(2*n-2*k) for k in (0..n)) for n in (2..27)] # Stefano Spezia, Apr 24 2023
CROSSREFS
Apparently the same as A038797, but with offset 2.
Cf. A038792.
Sequence in context: A213557 A273386 A045618 * A038797 A136530 A259033
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 02 2000
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 24 22:09 EDT 2024. Contains 372782 sequences. (Running on oeis4.)