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A036355
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Fibonacci-Pascal triangle read by rows.
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12
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1, 1, 1, 2, 2, 2, 3, 5, 5, 3, 5, 10, 14, 10, 5, 8, 20, 32, 32, 20, 8, 13, 38, 71, 84, 71, 38, 13, 21, 71, 149, 207, 207, 149, 71, 21, 34, 130, 304, 478, 556, 478, 304, 130, 34, 55, 235, 604, 1060, 1390, 1390, 1060, 604, 235, 55, 89, 420, 1177, 2272, 3310, 3736, 3310
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| T(n, m)=T'(n-1, m-1)+T'(n-2, m-2)+T'(n-1, m)+T'(n-2, m), where T'(n, m)=T(n, m) if 0<=m<=n and n >= 0 and T'(n, m)=0 otherwise. Initial term T(0, 0)=1.
T(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(2,0),(0,1),(0,2). [Joerg Arndt, Jun 30, 2011]
G.f.: 1/(1-(1+y)*x-(1+y^2)*x^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 11 2003
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EXAMPLE
| Triangle begins
1;
1, 1;
2, 2, 2;
3, 5, 5, 3;
5, 10, 14, 10, 5;
8, 20, 32, 32, 20, 8;
13, 38, 71, 84, 71, 38, 13;
21, 71, 149, 207, 207, 149, 71, 21;
34, 130, 304, 478, 556, 478, 304, 130, 34;
55, 235, 604, 1060, 1390, 1390, 1060, 604, 235, 55;
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MATHEMATICA
| nmax = 11; t[n_, m_] := t[n, m] = tp[n-1, m-1] + tp[n-2, m-2] + tp[n-1, m] + tp[n-2, m]; tp[n_, m_] /; 0 <= m <= n && n >= 0 := t[n, m]; tp[n_, m_] = 0; t[0, 0] = 1; Flatten[ Table[t[n, m], {n, 0, nmax}, {m, 0, n}]] (* From Jean-François Alcover, Nov 09 2011, after formula *)
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PROG
| (PARI) /* same as in A092566 but use */
steps=[[1, 0], [2, 0], [0, 1], [0, 2]];
/* Joerg Arndt, Jun 30 2011 */
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CROSSREFS
| Row sums form sequence A002605. T(n, 0) forms the Fibonacci sequence (A000045). T(n, 1) forms sequence A001629.
Derived sequences: A036681, A036682, A036683, A036684, A036692.
Sequence in context: A114639 A071867 A126337 * A095972 A091974 A029073
Adjacent sequences: A036352 A036353 A036354 * A036356 A036357 A036358
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KEYWORD
| nonn,tabl,easy,nice
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com), Dec 28 1998
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