OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Hung Viet Chu, Partial Sums of the Fibonacci Sequence, arXiv:2106.03659 [math.CO], 2021.
Ligia Loretta Cristea, Ivica Martinjak, and Igor Urbiha, Hyperfibonacci Sequences and Polytopic Numbers, arXiv:1606.06228 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (5,-9,6,1,-3,1).
FORMULA
a(n) = Fibonacci(n+8) - (n^3 +12*n^2 +59*n +126)/6.
G.f.: x/((1-x)^4*(1-x-x^2)).
MAPLE
with(combinat); seq(fibonacci(n+8)-(n^3+12*n^2+59*n+126)/6, n = 0..30); # G. C. Greubel, Sep 06 2019
MATHEMATICA
Nest[Accumulate, Fibonacci[Range[0, 30]], 4] (* Jean-François Alcover, Jan 08 2019 *)
PROG
(PARI) a(n)=fibonacci(n+8)-(n^3+12*n^2+59*n+126)/6 \\ Charles R Greathouse IV, Jun 11 2015
(Magma) [Fibonacci(n+8)-(n^3+12*n^2+59*n+126)/6: n on [0..30]]; // G. C. Greubel, Sep 06 2019
(Sage) [fibonacci(n+8)-(n^3+12*n^2+59*n+126)/6 for n in (0..30)] # G. C. Greubel, Sep 06 2019
(GAP) List([0..30], n-> Fibonacci(n+8)-(n^3+12*n^2+59*n+126)/6); # G. C. Greubel, Sep 06 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved