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A003099 a(n) = Sum_{k=0..n} C(n,k^2).
(Formerly M0576)
17
1, 2, 3, 4, 6, 11, 22, 43, 79, 137, 231, 397, 728, 1444, 3018, 6386, 13278, 26725, 51852, 97243, 177671, 320286, 579371, 1071226, 2053626, 4098627, 8451288, 17742649, 37352435, 77926452, 159899767, 321468048, 632531039, 1219295320, 2308910353, 4314168202 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..35.

Henry W. Gould, Fibonomial Catalan numbers: arithmetic properties and a table of the first fifty numbers, Abstract 71T-A216, Notices Amer. Math. Soc, 1971, page 938. [Annotated scanned copy of abstract]

Henry W. Gould, Letter to N. J. A. Sloane, Nov 1973, and various attachments.

Henry W. Gould, Letters to N. J. A. Sloane, Oct 1973 and Jan 1974.

FORMULA

a(n)*sqrt(n)/2^n is bounded: lim sup a(n)*sqrt(n)/2^n = 0.82... and lim inf a(n)*sqrt(n)/2^n = 0.58... - Benoit Cloitre, Nov 14 2003

Binomial transform of the characteristic function of squares A010052. - Carl Najafi, Sep 09 2011

MATHEMATICA

Table[Sum[Binomial[n, k^2], {k, 0, Sqrt[n]}], {n, 0, 50}] (* T. D. Noe, Sep 10 2011 *)

PROG

(PARI) a(n)=sum(k=0, sqrtint(n), binomial(n, k^2)) \\ Charles R Greathouse IV, Mar 26 2013

CROSSREFS

Sequence in context: A117308 A114412 A016038 * A061941 A029505 A185092

Adjacent sequences:  A003096 A003097 A003098 * A003100 A003101 A003102

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Henry W. Gould

EXTENSIONS

More terms from Carl Najafi, Sep 09 2011

STATUS

approved

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Last modified February 20 08:44 EST 2019. Contains 320325 sequences. (Running on oeis4.)