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Search: id:A035507
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| A035507 |
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Inverse Stolarsky array read by antidiagonals. |
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+0
6
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| 1, 2, 4, 3, 7, 12, 5, 9, 20, 33, 6, 14, 25, 54, 88, 8, 17, 38, 67, 143, 232, 10, 22, 46, 101, 177, 376, 609, 11, 27, 59, 122, 266, 465, 986, 1596, 13, 30, 72, 156, 321, 698, 1219, 2583, 4180, 15, 35, 80, 190, 410, 842, 1829, 3193, 6764, 10945, 16, 41, 93, 211, 499
(list; table; graph; listen)
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OFFSET
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0,2
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REFERENCES
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C. Kimberling, "Interspersions and dispersions," Proceedings of the American Mathematical Society 117 (1993) 313-321.
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LINKS
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C. Kimberling, Interspersions
N. J. A. Sloane, Classic Sequences
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FORMULA
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The term in row n and column k of the inverse Stolarsky array has the following expression: a(n, k)= F(2k-3)-1-c1(n)F(2k-4)+c2(n)F(2k-2), where F is the Fibonacci sequence; c1(n)=1 if n=1, [(n-1)*tau] if n>1 (first column of the Inverse Stolarsky array) and c2(n)=c1(n)+1+floor((2*c1(n)+1)*tau/2) (second column of the Inverse Stolarsky array). tau=(1+sqrt(5))/2 and [] denotes the nearest integer function. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 31 2004
Also, the following recurrence holds: a(n, k)=3*a(n, k-1)-a(n, k-2)+1 with a(n, 1)=c1(n) and a(n, 2)=c2(n). - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 31 2004
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EXAMPLE
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Top left hand corner of array:
1 4 12 33 88 232...
2 7 20 54 143 376...
3 9 25 67 177 465...
5 14 38 101 266 698...
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MAPLE
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with(combinat, fibonacci): gold:=(1+sqrt(5))/2: c1:=n->piecewise(n<>1, round((n-1)*gold), 1): c2:=n->c1(n)+floor((2*c1(n)+1)*gold/2)+1: inv_stol:=(n, k)->fibonacci(2*k-3)-1-c1(n)*fibonacci(2*k-4)+c2(n)*fibonacci(2*k-2): seq(seq(inv_stol(n+1-k, k), k=1..n), n=1..11); inv_stol2:=(n, k)->(1+c0(n))*fibonacci(2*k-3)+(1+floor((2*c0(n)+1)*gold/2))*fibonacci(2*k-2)-1:\ seq(seq(inv_stol2(n+1-k, k), k=1..n), n=1..11); (Ronaldo)
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CROSSREFS
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Cf. A035506.
Sequence in context: A101267 A090568 A166017 this_sequence A138612 A058330 A124256
Adjacent sequences: A035504 A035505 A035506 this_sequence A035508 A035509 A035510
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KEYWORD
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nonn,tabl,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 31 2004
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