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 A088803 a(n) gives the number of steps taken in a process which manipulates piles of tokens arranged in a line. There are 2n (or 2n+1) tokens in all. Initially they are all in one pile. At each step every pile with more than 1 token is divided into two and half the token are added to the pile on the left and half to the pile on the right. If a pile has an odd number of tokens, the token left over stays where it is. The redistributions in each step are done in parallel. 2
 1, 3, 7, 11, 17, 25, 33, 41, 53, 65, 77, 93, 109, 123, 143, 163, 181, 203, 227, 249, 277, 303, 329, 357, 389, 417, 451, 485, 517, 555, 593, 629, 669, 711, 749, 795, 839, 883, 931, 981, 1025, 1077, 1131, 1179, 1235, 1293, 1343, 1403, 1465, 1519, 1583, 1649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..52. R. Anderson, L. Lovász, P. Shor, J. Spencer, E. Tardos, S. Winograd, Disks, balls and walls: analysis of a combinatorial game, Amer. Math. Monthly, 6, 96, pp. 481-493, 1989. FORMULA The sequence is asymptotically quadratic with a(n) ~= c*n^2, where c is between 0.33 and 0.65, with estimate 0.5973 for n = 10000. EXAMPLE E.g., a(2) = 3 because there are 3 steps in the process beginning with 4 tokens: 0 0 4 0 0 0 2 0 2 0 1 0 2 0 1 1 1 0 1 1 PROG (C) #include #include #define N 1000 #define NN (2 * (N / 2) + 1) void e(int *t, int *T) { int i; for (i = 0; i < NN; i ++) { T[i] += (t[i] % 2); int f = (t[i] / 2); if (f) { T[i - 1] += f; T[i + 1] += f; } } } int f(int n) { int t[NN], T[NN], i = 0; memset(t, 0, sizeof(t)); memset(T, 0, sizeof(T)); t[N / 2] = n; e(t, T); while (memcmp(t, T, sizeof(t)) != 0) { i ++; memcpy(t, T, sizeof(T)); memset(T, 0, sizeof(T)); e(t, T); } return i; } int main() { int n; for (n = 2; n <= N; n += 2) { printf("%d, ", f(n)); fflush(stdout); } printf("\n"); } /* Luc Rousseau, Jun 29 2018 */ CROSSREFS Cf. A088804. Sequence in context: A294479 A331968 A029715 * A350146 A194069 A088206 Adjacent sequences: A088800 A088801 A088802 * A088804 A088805 A088806 KEYWORD nonn AUTHOR Rob Arthan, Oct 17 2003 STATUS approved

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Last modified November 30 01:30 EST 2023. Contains 367452 sequences. (Running on oeis4.)