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A370174
Triangle read by rows: Riordan array (1/(1 - x), x*(1 + x)/(1 - x - x^2)).
7
1, 1, 1, 1, 3, 1, 1, 6, 5, 1, 1, 11, 15, 7, 1, 1, 19, 37, 28, 9, 1, 1, 32, 82, 87, 45, 11, 1, 1, 53, 170, 234, 169, 66, 13, 1, 1, 87, 337, 573, 535, 291, 91, 15, 1, 1, 142, 647, 1314, 1511, 1061, 461, 120, 17, 1, 1, 231, 1213, 2871, 3933, 3398, 1904, 687, 153, 19, 1
OFFSET
0,5
FORMULA
T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1), T(n,0) = 1, T(n,k) = 0 if k > n.
Sum_{k = 0..n} T(n,k)* x^k = A000012(n), A057960(n), A196472(n+1), A218988(n-1) for x = 0, 1, 2, 3 respectively.
EXAMPLE
Triangle T(n,k) begins:
k=0 1 2 3 4 5 6
n=0: 1;
n=1: 1, 1;
n=2: 1, 3, 1;
n=3: 1, 6, 5, 1;
n=4: 1, 11, 15, 7, 1;
n=5: 1, 19, 37, 28, 9, 1;
n=6: 1, 32, 82, 87, 45, 11, 1;
...
87 = 28 + 37 + 7 + 15.
CROSSREFS
Cf. A000012 (column k=0), A000384, A001911, A005408.
Cf. A057960 (row sums), A196472, A218988.
Sequence in context: A145904 A273350 A328083 * A278132 A203950 A273349
KEYWORD
nonn,tabl,easy
AUTHOR
Philippe Deléham, Feb 29 2024
STATUS
approved