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A275580 Add square root of sum of terms. 1
1, 2, 3, 5, 8, 12, 17, 23, 31, 41, 52, 65, 81, 99, 119, 142, 168, 197, 229, 264, 303, 346, 392, 442, 497, 556, 619, 687, 760, 838, 921, 1009, 1103, 1203, 1308, 1419, 1537, 1661, 1791, 1928, 2072, 2223, 2381, 2546, 2719, 2900, 3088 (list; graph; refs; listen; history; text; internal format)
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

Sequence in context: A022856 A089071 A177205 * A175829 A241552 A175827

Adjacent sequences:  A275577 A275578 A275579 * A275581 A275582 A275583

KEYWORD

easy,nonn

AUTHOR

Hugo van der Sanden, Aug 02 2016

STATUS

approved

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Last modified July 25 03:53 EDT 2021. Contains 346283 sequences. (Running on oeis4.)