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1, 1, 1, 1, -6, 1, 1, -6, -6, 1, 1, -55, -55, -55, 1, 1, -104, -153, -153, -104, 1, 1, -496, -594, -643, -594, -496, 1, 1, -1231, -1721, -1819, -1819, -1721, -1231, 1, 1, -4710, -5935, -6425, -6474, -6425, -5935, -4710, 1, 1, -13334, -18038, -19263, -19704, -19704, -19263, -18038, -13334, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Row sums are s(n) = {1, 2, -4, -10, -163, -512, -2821, -9540, -40612, -140676, -537533, ...} where s(n) = 3*s(n-1) +11*s(n-2) -27*s(n-3) -35*s(n-4) +49*s(n-5) with g.f. (1-x-21*x^2+7*x^3)/((1-x)*(1-x-7*x^2)^2).
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LINKS
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FORMULA
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T(n,k) = T(n,n-k).
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, -6, 1;
1, -6, -6, 1;
1, -55, -55, -55, 1;
1, -104, -153, -153, -104, 1;
1, -496, -594, -643, -594, -496, 1;
1, -1231, -1721, -1819, -1819, -1721, -1231, 1;
1, -4710, -5935, -6425, -6474, -6425, -5935, -4710, 1;
1, -13334, -18038, -19263, -19704, -19704, -19263, -18038, -13334, 1;
1, -46311, -59639, -64343, -65519, -65911, -65519, -64343, -59639, -46311, 1;
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MATHEMATICA
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(* Set of sequences q=0..10 *)
f[n_, q_]:= f[n, q] = If[n<2, n, f[n-1, q] + q*f[n-2, q]];
T[n_, k_, q_]:= f[k+1, q] + f[n-k+1, q] - f[n+1, q];
Table[Flatten[Table[T[n, k, q], {n, 0, 10}, {k, 0, n}], {q, 0, 10}]
(* Second program *)
A015442[n_]:= Sum[7^j*Binomial[n-j, j], {j, 0, (n+1)/2}]; T[n_, k_]:= T[n, k]= A015442[k] +A015442[n-k] -A015442[n]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 24 2019 *)
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PROG
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(PARI) A015442(n) = sum(j=0, (n+1)\2, 7^j*binomial(n-j, j));
(Magma) A015442:= func< n | &+[7^j*Binomial(n-j, j): j in [0..Floor(n/2)]] >;
(Sage)
def A015442(n): return sum(7^j*binomial(n-j, j) for j in (0..floor(n/2)))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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