OFFSET
0,2
COMMENTS
a(0) = 1; a(n) = a(n-1) + floor(sqrt(Sum_{i=0..n-1} a(i))).
This appears to give asymptotically a(n) = n^3/36, sum of terms n^4/144, regardless of the starting value a(0).
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Robert Israel, Formulas for A275580
Christian Krause, LODA
Index entries for linear recurrences with constant coefficients, signature (3,-4,5,-6,5,-4,3,-1).
FORMULA
G.f.: (1-x+x^2-x^3+x^4)/((1-x)^3(1+x^2-x^3-x^5)). See link "Formulas for A275580". - Robert Israel, Aug 09 2016
a(n) = n + 1 + Sum_{i=0..n} floor((floor(i^2 / 3) + i) / 4); derived from corresponding LODA program (see link). - Hugo van der Sanden, Feb 24 2021
EXAMPLE
a(3) = a(2) + floor(sqrt(1 + 2)) = 2 + 1 = 3;
a(4) = a(3) + floor(sqrt(1 + 2 + 3)) = 3 + 2 = 5.
MAPLE
G:= (x^4-x^3+x^2-x+1)/((x^5+x^3-x^2-1)*(x-1)^3):
S:= series(G, x, 101):
seq(coeff(S, x, j), j=0..100); # Robert Israel, Aug 09 2016
MATHEMATICA
a = {1}; Do[AppendTo[a, a[[k]] + Floor@ Sqrt@ Total@ a], {k, 46}]; a (* Michael De Vlieger, Aug 03 2016 *)
PROG
(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = va[n-1] + floor(sqrt(sum(k=1, n-1, va[k]))); ); va; } \\ Michel Marcus, Aug 02 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Hugo van der Sanden, Aug 02 2016
STATUS
approved