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A140993
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Triangle read by rows: recurrence G(n,k): G(n, n)=G(n+1, 1)=1, G(n+2, 2)=2, G(n+3, k)=G(n+1, k-1)+G(n+1, k-2)+G(n+2, k-1) for k:=2..(n+2), 0<=k<=n.
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2
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1, 1, 1, 1, 2, 1, 1, 2, 4, 1, 1, 2, 5, 7, 1, 1, 2, 5, 11, 12, 1, 1, 2, 5, 12, 23, 20, 1, 1, 2, 5, 12, 28, 46, 33, 1, 1, 2, 5, 12, 29, 63, 89, 54, 1, 1, 2, 5, 12, 29, 69, 137, 168, 88, 1, 1, 2, 5, 12, 29, 70, 161, 289, 311, 143, 1, 1, 2, 5, 12, 29, 70, 168, 367, 594, 567, 232, 1, 1, 2, 5, 12
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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EXAMPLE
| Triangle begins:
1
1 1
1 2 1
1 2 4 1
1 2 5 7 1
1 2 5 11 12 1
1 2 5 12 23 20 1
1 2 5 12 28 46 33 1
1 2 5 12 29 63 89 54 1
1 2 5 12 29 69 137 168 88 1
1 2 5 12 29 70 161 289 311 143 1
1 2 5 12 29 70 168 367 594 567 232 1
1 2 5 12 29 70 169 399 817 1194 1021 376 1
1 2 5 12 29 70 169 407 934 1778 2355 1820 609 1
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MAPLE
| A140993 := proc(n, k) if k = n then 1; elif k = 1 then 1; elif k = 2 then 2; else procname(n-2, k-1)+procname(n-2, k-2)+procname(n-1, k-1) ; end if; end proc: seq(seq(A140993(n, k), k=1..n), n=1..15) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2010]
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MATHEMATICA
| t[n_, k_] := If[k == n, 1, If[k == 1, 1, If[k == 2, 2, t[n - 2, k - 1] + t[n - 2, k - 2] + t[n - 1, k - 1]]]]; Flatten[Table[ t[n, k], {n, 13}, {k, n}]] (* Robert G. Wilson v, (rgwv@rgwv.com) 22 Dec 2011 *)
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CROSSREFS
| Cf. A007318.
Sequence in context: A140995 A141021 A140994 * A027935 A137940 A137855
Adjacent sequences: A140990 A140991 A140992 * A140994 A140995 A140996
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KEYWORD
| nonn,tabl
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AUTHOR
| Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jul 08 2008
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EXTENSIONS
| Entries checked by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 28 2010
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