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A141043
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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-2th and i-3th terms.
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0
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1, 4, 9, 31, 88, 288, 889, 2884, 9211, 29976, 97296, 318371, 1042756, 3429604, 11298969, 37320679, 123473176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| May coincide with a(n)=sum{k-0..n, C(k,n-k)C(2n-k,n)}. [From Paul Barry (pbarry(AT)wit.ie), Dec 02 2008]
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REFERENCES
| Romanian Informatics Olympiad, 2001
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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).
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PROG
| #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(input, "%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; }
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CROSSREFS
| Sequence in context: A041137 A042599 A145543 * A111160 A192876 A201689
Adjacent sequences: A141040 A141041 A141042 * A141044 A141045 A141046
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KEYWORD
| nonn
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AUTHOR
| Shravas Rao (shravas(AT)gmail.com), Jul 30 2008
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