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A140993 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. 2
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; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..81.

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

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) ; # R. J. Mathar, Apr 28 2010

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, Dec 22 2011 *)

CROSSREFS

Cf. A007318.

Sequence in context: A141021 A140994 A245163 * A027935 A137940 A274859

Adjacent sequences:  A140990 A140991 A140992 * A140994 A140995 A140996

KEYWORD

nonn,tabl

AUTHOR

Juri-Stepan Gerasimov, Jul 08 2008

EXTENSIONS

Entries checked by R. J. Mathar, Apr 28 2010

STATUS

approved

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Last modified June 28 05:07 EDT 2017. Contains 288813 sequences.