A362067 Sum of successive Fibonacci numbers F(n) : a(n) = Sum_{k = 0..n} F(n+k).

0, 2, 6, 18, 50, 136, 364, 966, 2550, 6710, 17622, 46224, 121160, 317434, 831430, 2177322, 5701290, 14927768, 39083988, 102327390, 267903350, 701391022, 1836283246, 4807480608, 12586194000, 32951158706, 86267374854, 225851115906, 591286215650, 1548007923880

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

Formula

a(n) = 4*a(n-1)-3*a(n-2)-2*a(n-3)+a(n-4), a(0)=0, a(1)=2, a(2)=6, a(3)=18.

G.f.: 2*x*(1-x)/((1-3*x+x^2)*(1-x-x^2)).

a(n) = A000045(2n+2) - A000045(n+1).

a(n) = 2 * A094292(n+1). - Alois P. Heinz, Apr 07 2023

Example

a(n) are the row sums of the triangle T(n,k) (A199334):
0 ;
1 , 1 ;
1 , 2 , 3 ;
2 , 3 , 5 , 8 ;
3 , 5 , 8 , 13, 21 ;
5 , 8 ,13 , 21, 34 , 55 ;
..........................
T(n,k) = T(n,k-1) + T(n-1, k-1) ; T(n,0) = A000045(n).

Crossrefs

Cf. A000045, A094292, A199334.

Sequence in context: A048495 A089380 A271897 * A304962 A372481 A361286

Adjacent sequences: A362064 A362065 A362066 * A362068 A362069 A362070

Keyword

nonn,easy

Author

Philippe Deléham, Apr 07 2023

Status

approved