A278288 a(n) is the number of ways to represent a(n-1) as a sum of two distinct terms from a(0) to a(n-2). a(0) = 0. a(1) = a(2) = 1.

0, 1, 1, 1, 2, 3, 3, 4, 6, 2, 4, 8, 3, 8, 4, 12, 6, 10, 10, 11, 12, 15, 9, 12, 19, 7, 15, 17, 10, 18, 22, 17, 12, 22, 21, 22, 25, 25, 26, 22, 26, 26, 27, 32, 25, 30, 27, 35, 21, 23, 31, 31, 32, 37, 37, 38, 37, 39, 37, 40, 40, 41, 45, 28, 37, 42, 38, 50, 33, 43, 58, 34

Offset

0,5

Comments

a(n) is the number of pairs (j, k) such that a(j) + a(k) = a(n-1), with 0 <= j, k < n-1 and j != k.

For large n, a(n) on average follows linear law a(n) ~ 0.7 n with linear spread (see the plot).

Unlike sequences such as A248034 or A276457, this sequence is base-independent.

Links

Yuriy Sibirmovsky, Table of n, a(n) for n = 0..2999

Yuriy Sibirmovsky, The plot of a(n) for n=0..2999 (with linear regression)

Example

a(2) = a(1) + a(0), so a(3) = 1.
a(3) = a(1) + a(0) = a(2) + a(0), so a(4) = 2.
a(4) = a(3) + a(2) = a(3) + a(1) = a(2) + a(1), so a(5) = 3.

Mathematica

Nm=100;
A=Table[1, {n, 1, Nm}];
A[[1]]=0;
Do[Nc=0;
Do[If[A[[j]]+A[[k]]==A[[n]] && k!=j, Nc++], {j, 1, n-1}, {k, 1, j}];
A[[n+1]]=Nc, {n, 3, Nm-1}];
A

Crossrefs

Cf. A248034, A276457.

Sequence in context: A238394 A372595 A182503 * A023154 A358073 A070820

Adjacent sequences: A278285 A278286 A278287 * A278289 A278290 A278291

Keyword

nonn

Author

Yuriy Sibirmovsky, Nov 16 2016

Status

approved