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A177011
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Define two triangular arrays by: B(0,0)=C(0,0)=1, B(0,r)=C(0,r)=0 for r>0, C(t,-1)=C(t,0); and for t,r >= 0, B(t+1,r)=C(t,r-1)+2C(t,r)-B(t,r), C(t+1,r)=B(t+1,r)+2B(t+1,r+1)-C(t,r). Sequence gives array B(t,r) read by rows.
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5
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1, 2, 1, 7, 4, 1, 29, 18, 6, 1, 130, 85, 33, 8, 1, 611, 414, 177, 52, 10, 1, 2965, 2062, 943, 313, 75, 12, 1, 14726, 10447, 5023, 1817, 501, 102, 14, 1, 74443, 53650, 26818, 10348, 3152, 749, 133, 16, 1, 381617, 278568, 143655, 58305, 19147, 5080, 1065, 168, 18, 1
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OFFSET
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0,2
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LINKS
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EXAMPLE
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Triangle begins
1
2 1
7 4 1
29 18 6 1
130 85 33 8 1
611 414 177 52 10 1
...
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MAPLE
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B:=proc(t, r)global b:if(not type(b[t, r], integer))then if(t=0 and r=0)then b[t, r]:=1:elif(t=0)then b[t, r]:=0:else b[t, r]:=C(t-1, r-1)+2*C(t-1, r)-B(t-1, r):fi:fi:return b[t, r]:end:
C:=proc(t, r)global c:if(not type(c[t, r], integer))then if(r=-1)then return C(t, 0):fi:if(t=0 and r=0)then c[t, r]:=1:elif(t=0)then c[t, r]:=0:else c[t, r]:=B(t, r)+2*B(t, r+1)-C(t-1, r):fi:fi:return c[t, r]:end:
for t from 0 to 9 do for r from 0 to t do print(B(t, r)):od:od: # Nathaniel Johnston, Apr 15 2011
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MATHEMATICA
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bb[t_, r_] := Module[{}, If[Not[IntegerQ[b[t, r]]], Which[t == 0 && r == 0, b[t, r] = 1, t == 0, b[t, r] = 0, True, b[t, r] = cc[t-1, r-1] + 2*cc[t-1, r] - bb[t-1, r]]]; Return[b[t, r]]]; cc[t_, r_] := Module[{}, If[Not[IntegerQ[c[t, r]]], If[r == -1, Return[cc[t, 0]], Which[t == 0 && r == 0, c[t, r] = 1, t == 0, c[t, r] = 0, True, c[t, r] = bb[t, r] + 2*bb[t, r+1] - cc[t-1, r]]]]; Return[c[t, r]]]; Table[bb[t, r], {t, 0, 9}, {r, 0, t}] // Flatten (* Jean-François Alcover, Jan 08 2014, translated from Maple *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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