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A131025
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Antidiagonal sums of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j-1,k) for 2 <= k <= j.
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5
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1, 1, 3, 2, 5, 3, 9, 6, 16, 11, 27, 22, 50, 50, 101, 114, 215, 255, 471, 552, 1024, 1145, 2169, 2290, 4460, 4460, 8921, 8556, 17477, 16383, 33861, 31674, 65536, 62255, 127791, 124510, 252302, 252302, 504605, 514446, 1019051, 1048575, 2067627
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f.: (1-3*x^2+2*x^4+2*x^6-2*x^8+x^9)/((1-x)*(1+x)*(1-x+x^2)*(1-2*x^2)*(1-3*x^2+3*x^4)).
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EXAMPLE
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MATHEMATICA
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CoefficientList[Series[(1 - 3 x^2 + 2 x^4 + 2 x^6 - 2 x^8 + x^9)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - 2 x^2)*(1 - 3 x^2 + 3 x^4)), {x, 0, 42}], x] (* Michael De Vlieger, Oct 26 2021 *)
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PROG
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(PARI) {m=43; M=matrix(m, m); for(j=1, m, M[j, 1]=if((j-1)%6<3, 1, 0)); for(k=2, m, for(j=k, m, M[j, k]=M[j-1, k-1]+M[j, k-1])); for(j=1, m, print1(sum(k=1, (j+1)\2, M[j-k+1, k]), ", "))}
(Magma) m:=43; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) mod 6 lt 3 then M[j, 1]:=1; end if; end for; for k:=2 to m do for j:=k to m do M[j, k]:=M[j-1, k-1]+M[j, k-1]; end for; end for; [ &+[ M[j-k+1, k]: k in [1..(j+1) div 2] ]: j in [1..m] ];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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