cp's OEIS Frontend

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.

%I A278288 #8 Nov 24 2016 09:53:13
%S A278288 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,
%T A278288 18,22,17,12,22,21,22,25,25,26,22,26,26,27,32,25,30,27,35,21,23,31,31,
%U A278288 32,37,37,38,37,39,37,40,40,41,45,28,37,42,38,50,33,43,58,34
%N 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.
%C A278288 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.
%C A278288 For large n, a(n) on average follows linear law a(n) ~ 0.7 n with linear spread (see the plot).
%C A278288 Unlike sequences such as A248034 or A276457, this sequence is base-independent.
%H A278288 Yuriy Sibirmovsky, <a href="/A278288/b278288.txt">Table of n, a(n) for n = 0..2999</a>
%H A278288 Yuriy Sibirmovsky, <a href="/A278288/a278288.png">The plot of a(n) for n=0..2999 (with linear regression)</a>
%e A278288 a(2) = a(1) + a(0), so a(3) = 1.
%e A278288 a(3) = a(1) + a(0) = a(2) + a(0), so a(4) = 2.
%e A278288 a(4) = a(3) + a(2) = a(3) + a(1) = a(2) + a(1), so a(5) = 3.
%t A278288 Nm=100;
%t A278288 A=Table[1,{n,1,Nm}];
%t A278288 A[[1]]=0;
%t A278288 Do[Nc=0;
%t A278288 Do[If[A[[j]]+A[[k]]==A[[n]] && k!=j,Nc++],{j,1,n-1},{k,1,j}];
%t A278288 A[[n+1]]=Nc,{n,3,Nm-1}];
%t A278288 A
%Y A278288 Cf. A248034, A276457.
%K A278288 nonn
%O A278288 0,5
%A A278288 _Yuriy Sibirmovsky_, Nov 16 2016