OFFSET
0,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 0..10000
Arnold Knopfmacher and Florian Luca, Digit sums of binomial sums, Journal of Number Theory, Vol. 132, No. 2 (2012), pp. 324-331.
Florian Luca and Igor E. Shparlinski, On the g-ary expansions of Apéry, Motzkin, Schröder and other combinatorial numbers, Annals of Combinatorics, Vol. 14 (2010), pp. 507-524.
FORMULA
a(n) > c * (log(n)/log(log(n)))^(1/4) holds on a set of n of asymptotic density 1, where c > 0 is a constant (Luca and Shparlinski, 2010).
a(n) > c * log(n)/log(log(n)) holds on a set of n of asymptotic density 1, where c > 0 is a constant (Knopfmacher and Luca, 2012).
Conjecture: Limit_{m->oo} (1/m^2) * Sum_{k=1..m} a(k) = log(sqrt(2) + 1)/log(2) = 1.2715533... (Knopfmacher and Luca, 2012).
MATHEMATICA
a[n_] := DigitCount[Sum[(Binomial[n, k] * Binomial[n+k, k])^2, {k, 0, n}], 2, 1]; Array[a, 100, 0]
PROG
(PARI) a(n) = hammingweight(sum(k=0, n, (binomial(n, k)*binomial(n+k, k))^2));
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Amiram Eldar, Dec 17 2024
STATUS
approved
