A141043 Number of sequences of length n whose terms are positive integers less than or equal to n in which the i-th term is greater than both the (i-2)nd and (i-3)rd terms.

1, 4, 9, 31, 88, 288, 889, 2884, 9211, 29976, 97296, 318371, 1042756, 3429604, 11298969, 37320679, 123473176

Offset

1,2

Comments

Apparently a(n) = sum(k=0..n, C(k, n-k)*C(2*n-k, n) ). - Paul Barry, Dec 02 2008

References

Romanian Informatics Olympiad, 2001

Links

Table of n, a(n) for n=1..17.

Example

The valid sequences for n = 3 are (1, 1, 2), (1, 1, 3), (1, 2, 2), (1, 2, 3), (1, 3, 2), (1, 3, 3), (2, 1, 3), (2, 2, 3), (2, 3, 3).

Prog

(C)
#include <stdio.h>
#define MAX_N 1001
int N;
int DP[MAX_N][MAX_N], X[MAX_N][MAX_N];
int main() {
    int i, j;
    scanf("%d ", &N);
    for(i = 1; i <= N; i++) { DP[1][i] = i; DP[2][i] = i * i; }
    for(i = 3; i <= N; i++) {
        for(j = 1; j <= N; j++) {
            if(j - 2 >= 0) X[i][j] = X[i][j - 1] + DP[i - 2][j - 2];
            DP[i][j] = DP[i][j - 1] + DP[i - 1][j - 1]
                          + DP[i - 2][j - 1] + X[i][j];
        }
    }
    printf("%d ", DP[N][N]);
    return 0;
}

Crossrefs

Sequence in context: A042599 A206960 A145543 * A111160 A192876 A201689

Adjacent sequences: A141040 A141041 A141042 * A141044 A141045 A141046

Keyword

nonn,more

Author

Shravas Rao, Jul 30 2008

Status

approved