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A106595
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Triangle read by rows: odd-numbered rows of A106580.
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3
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1, 1, 1, 2, 3, 3, 1, 2, 5, 9, 12, 12, 1, 2, 5, 13, 26, 41, 53, 53, 1, 2, 5, 13, 34, 73, 129, 194, 247, 247, 1, 2, 5, 13, 34, 89, 201, 386, 645, 945, 1192, 1192, 1, 2, 5, 13, 34, 89, 233, 546, 1117, 2021, 3266, 4705, 5897, 5897, 1, 2, 5, 13, 34, 89, 233, 610, 1469, 3157, 6082, 10593, 16737, 23826, 29723, 29723
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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Irregular triangle begins as:
1, 1;
1, 2, 3, 3;
1, 2, 5, 9, 12, 12;
1, 2, 5, 13, 26, 41, 53, 53;
1, 2, 5, 13, 34, 73, 129, 194, 247, 247;
1, 2, 5, 13, 34, 89, 201, 386, 645, 945, 1192, 1192;
1, 2, 5, 13, 34, 89, 233, 546, 1117, 2021, 3266, 4705, 5897, 5897;
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MAPLE
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A106580 := proc(n, k) option remember ; if k =0 then 1 ; else A106580(n, k-1)+add(A106580(n-2*i, k-i), i=1..min(k, floor(n/2), n-k)) ; fi ; end: for n from 1 to 13 by 2 do for k from 0 to n do printf("%d, ", A106580(n, k)) ; od ; od ; # R. J. Mathar, May 02 2007
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[k==0, 1, T[n, k-1] + Sum[T[n-2*j, k-j], {j, 1, Min[k, Floor[n/2], n-k]}]]; (* T(n, k) = A106580; T(2*n+1, k) = A106595 *)
Table[T[2*n+1, k], {n, 0, 12}, {k, 0, 2*n+1}]//Flatten (* G. C. Greubel, Sep 08 2021 *)
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PROG
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(Sage)
@CachedFunction
if (k<0): return 0
elif (k==0): return 1
else: return T(n, k-1) + sum( T(n-2*j, k-j) for j in (1..min(k, n//2, n-k)))
flatten([[T(2*n+1, k) for k in (0..2*n+1)] for n in (0..12)]) # G. C. Greubel, Sep 08 2021
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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