A325933 Partial sums of A325931.

0, 1, 2, 3, 4, 3, 4, 5, 4, 5, 4, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 7, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9, 8, 9

Offset: 0

Author

Allan C. Wechsler, Sep 08 2019

Keywords

• nonn
• easy

Comments

This sequence is the "tier profile" of A076042, much as A064289 provides a similar profile of Recamán's Sequence (A005132). In each case, the base sequence jumps around between adjacent "tiers", each of which changes value relatively slowly (compared to the difference between entries in different tiers). As in Recamán's sequence, each tier rises for a while, then crests, and finally falls close to zero, at which point that tier becomes extinct. The tier structure is salient when viewing the graph of such a sequence.

This sequence is less chaotic than A064289, since in A076042 only two tiers are active at time, and the sequence alternates between the two until the lower tier stops, at which point a double increase inaugurates a new tier.

Examples

			a(20) = a(19) + A325931(20) = 5 + 1 = 6.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..65536

Crossrefs

Cf. A076042, A325931.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 0, (t->
      t+`if`(tAlois P. Heinz, Sep 08 2019

Mathematica

b[n_] := b[n] = If[n == 0, 0, b[n - 1] + If[b[n - 1] < n^2, n^2, -n^2]];
b /@ Range[0, 105] // Differences // Sign // Accumulate // Prepend[#, 0]& (* Jean-François Alcover, Nov 30 2020 *)

Formula

a(0) = 0; a(n) = a(n-1) + A325931(n).