A358537 For n > 0, a(n) is the total number of terms in all contiguous subsequences of the terms up to a(n-1) that sum to n; a(0) = 1.
1, 1, 2, 2, 5, 4, 4, 2, 2, 5, 7, 8, 6, 11, 10, 16, 5, 22, 6, 19, 15, 22, 20, 9, 18, 5, 14, 16, 23, 9, 8, 11, 16, 12, 19, 21, 0, 21, 8, 20, 11, 17, 25, 28, 4, 18, 4, 30, 23, 40, 7, 20, 18, 18, 14, 9, 40, 9, 29, 32, 23, 6, 17, 23, 16, 8, 26, 32, 35, 27, 64, 10
Offset: 0
Examples
To find a(4), we look at the sequence so far (1, 1, 2, 2) to find contiguous subsequences that sum to 4: (1, 1, 2) and (2, 2). This is five terms in total, so a(4) = 5. Notice that the two subsequences overlap. a(40) is 11 because the following contiguous subsequences sum to 40: (6, 19, 15); (23, 9, 8); (19, 21); (19, 21, 0). This is a total of 11 terms.
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
-
Maple
N:= 100: V:= Array(0..N): V[0]:= 1: for n from 0 to N-1 do s:= 0; for j from n to 0 by -1 do s:= s + V[j]; if s > N then break fi; if s > n then V[s]:= V[s] + n-j+1 fi; od; od: convert(V,list); # Robert Israel, Feb 16 2023 -
PARI
{ for (n=1, #a=m=vector(72), print1 (a[n] = if (n==1, 1, m[n-1])", "); s = w = 0; forstep (k=n, 1, -1, w++; if ((s += a[k]) > #m, break, s, m[s] += w))) } \\ Rémy Sigrist, Feb 09 2023
Extensions
Data edited by Yifan Xie, Feb 08 2023
More terms from Rémy Sigrist, Feb 09 2023