A038737 T(n,n-2), array T as in A038792.

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

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