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Search: id:A067417
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| A067417 |
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Triangle with columns built from certain power sequences. |
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+0
10
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| 1, 3, 1, 9, 4, 1, 27, 24, 5, 1, 81, 144, 45, 6, 1, 243, 864, 405, 72, 7, 1, 729, 5184, 3645, 864, 105, 8, 1, 2187, 31104, 32805, 10368, 1575, 144, 9, 1, 6561, 186624, 295245, 124416, 23625, 2592, 189, 10, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The column sequences (without leading 0's) give: A000244 (powers of 3), A067411 for m=0..1 and A067419-24 for m=3..8. The third column (m=2) is A067403.
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FORMULA
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a(n, m)= 1 if n=m; a(n, m)= (m+3)*(3*(m+1))^(n-m-1) if n>m>=0, else 0.
G.f. for column m: (x^m)*(1-2*m*x)/(1-3*(m+1)*x).
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EXAMPLE
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{1}; {3,1}; {9,4,1}; {27,24,5,1}; ...
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CROSSREFS
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Cf. A009998 (triangle built from powers of (m+1)), A067402, A067410.
Sequence in context: A054448 A106516 A140071 this_sequence A016577 A124573 A127550
Adjacent sequences: A067414 A067415 A067416 this_sequence A067418 A067419 A067420
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KEYWORD
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nonn,easy,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jan 25 2002
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