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A014166
Apply partial sum operator 4 times to Fibonacci numbers.
15
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
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.
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
Right-hand column 8 of triangle A011794.
Sequence in context: A257199 A258473 A014161 * A014171 A014175 A097810
KEYWORD
nonn,easy
STATUS
approved