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A013610
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Triangle of coefficients in expansion of (1+3*x)^n.
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10
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1, 1, 3, 1, 6, 9, 1, 9, 27, 27, 1, 12, 54, 108, 81, 1, 15, 90, 270, 405, 243, 1, 18, 135, 540, 1215, 1458, 729, 1, 21, 189, 945, 2835, 5103, 5103, 2187, 1, 24, 252, 1512, 5670, 13608, 20412, 17496, 6561, 1, 27, 324, 2268, 10206, 30618, 61236, 78732
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| T(n,k) is the number of lattice paths from (0,0) to (n,k) with steps (1,0) and three kinds of steps (1,1). The number of paths with steps (1,0) and s kinds of steps (1,1) corresponds to the expansion of (1+s*x)^n. [Joerg Arndt, Jul 01 2011]
Mirror image of A027465. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 25 2007
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FORMULA
| G.f.: 1 / (1 - x*(1+3*y)).
Row sums are 4^n. [Joerg Arndt, Jul 01 2011]
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EXAMPLE
| Triangle begins
1;
1, 3;
1, 6, 9;
1, 9, 27, 27;
1, 12, 54, 108, 81;
1, 15, 90, 270, 405, 243;
1, 18, 135, 540, 1215, 1458, 729;
1, 21, 189, 945, 2835, 5103, 5103, 2187;
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PROG
| (PARI) T(n, k)=polcoeff((1+3*x)^n, k)
(PARI) /* same as in A092566 but use */
steps=[[1, 0], [1, 1], [1, 1], [1, 1]]; /* note triple [1, 1] */
/* Joerg Arndt, Jul 01 2011 */
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CROSSREFS
| The rows of A013610 are the rows of A027465 reversed.
Cf. A007318, A013609, A027465, etc.
Sequence in context: A074475 A144877 A049410 * A008573 A089710 A065918
Adjacent sequences: A013607 A013608 A013609 * A013611 A013612 A013613
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KEYWORD
| tabl,nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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