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A177020
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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 C(t,r) read by rows.
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3
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1, 3, 1, 12, 5, 1, 53, 25, 7, 1, 247, 126, 42, 9, 1, 1192, 642, 239, 63, 11, 1, 5897, 3306, 1330, 400, 88, 13, 1, 29723, 17187, 7327, 2419, 617, 117, 15, 1, 152020, 90099, 40187, 14233, 4033, 898, 150, 17, 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
3 1
12 5 1
53 25 7 1
247 126 42 9 1
1192 642 239 63 11 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 8 do for r from 0 to t do print(C(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[cc[t, r], {t, 0, 8}, {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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