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A053739 Partial sums of A014166. 10
1, 6, 22, 63, 155, 344, 709, 1383, 2587, 4685, 8273, 14323, 24416, 41119, 68595, 113590, 187030, 306605, 500950, 816410, 1327986, 2157046, 3499982, 5674578, 9195035, 14893364, 24115804, 39040633, 63192397, 102273950, 165512723, 267839033, 433410661, 701315739, 1134800215 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
LINKS
Hung Viet Chu, Partial Sums of the Fibonacci Sequence, arXiv:2106.03659 [math.CO], 2021.
FORMULA
a(n) = Sum_{i=0..floor(n/2)} binomial(n+5-i, n-2*i) for n >= 0.
a(n) = a(n-1) + a(n-2) + C(n+4,4); n >= 0; a(-1)=0.
G.f.: 1/((1-x-x^2)*(1-x)^5). - R. J. Mathar, May 22 2013
a(n) = Fibonacci(n+11) - (n^4 + 22*n^3 + 203*n^2 + 974*n + 2112)/4!. - G. C. Greubel, Sep 06 2019
MAPLE
with(combinat); seq(fibonacci(n+11)-(n^4 + 22*n^3 + 203*n^2 + 974*n + 2112)/4!, n = 0..35); # G. C. Greubel, Sep 06 2019
MATHEMATICA
Table[Fibonacci[n+11] -(n^4+22*n^3+203*n^2+974*n+2112)/4!, {n, 0, 35}] (* G. C. Greubel, Sep 06 2019 *)
PROG
(PARI) vector(35, n, m=n-1; fibonacci(n+10) - (m^4+22*m^3+203*m^2+974*m +2112)/4!) \\ G. C. Greubel, Sep 06 2019
(Magma) [Fibonacci(n+11) - (n^4+22*n^3+203*n^2+974*n+2112)/24: n in [0..35]]; // G. C. Greubel, Sep 06 2019
(Sage) [fibonacci(n+11) - (n^4+22*n^3+203*n^2+974*n+2112)/24 for n in (0..35)] # G. C. Greubel, Sep 06 2019
(GAP) List([0..35], n-> Fibonacci(n+11)-(n^4+22*n^3+203*n^2+974*n + 2112)/24); # G. C. Greubel, Sep 06 2019
CROSSREFS
Cf. A014166 and A000045.
Right-hand column 10 of triangle A011794.
Cf. A228074.
Sequence in context: A257200 A258474 A120477 * A280481 A055797 A001925
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Feb 13 2000
EXTENSIONS
Terms a(28) onward added by G. C. Greubel, Sep 06 2019
STATUS
approved

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Last modified April 24 18:17 EDT 2024. Contains 371962 sequences. (Running on oeis4.)