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!)
 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 Table of n, a(n) for n=2..27. Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1). 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 Adjacent sequences: A038734 A038735 A038736 * A038738 A038739 A038740 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.

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