A014166 Apply partial sum operator 4 times to Fibonacci numbers.

0, 1, 5, 16, 41, 92, 189, 365, 674, 1204, 2098, 3588, 6050, 10093, 16703, 27476, 44995, 73440, 119575, 194345, 315460, 511576, 829060, 1342936, 2174596, 3520457, 5698329, 9222440, 14924829, 24151764, 39081553

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

Cf. A000045, A228074, A136431.

Right-hand column 8 of triangle A011794.

Sequence in context: A257199 A258473 A014161 * A014171 A014175 A097810

Adjacent sequences: A014163 A014164 A014165 * A014167 A014168 A014169

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved