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A029618
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Numbers in (3,2)-Pascal triangle (by row).
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24
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1, 3, 2, 3, 5, 2, 3, 8, 7, 2, 3, 11, 15, 9, 2, 3, 14, 26, 24, 11, 2, 3, 17, 40, 50, 35, 13, 2, 3, 20, 57, 90, 85, 48, 15, 2, 3, 23, 77, 147, 175, 133, 63, 17, 2, 3, 26, 100, 224, 322, 308, 196, 80, 19, 2, 3, 29, 126, 324, 546, 630, 504, 276, 99, 21, 2, 3, 32, 155, 450, 870
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OFFSET
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0,2
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COMMENTS
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Triangle T(n,k), read by rows, given by (3,-2,0,0,0,0,0,0,0,...) DELTA (2,-1,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 10 2011
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LINKS
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FORMULA
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T(n,k) = T(n-1,k-1) + T(n-1,k) with T(0,0)=1, T(n,0)=3, T(n,n)=2; n, k > 0. - Boris Putievskiy, Sep 04 2013
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EXAMPLE
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Triangle begins as:
1;
3, 2;
3, 5, 2;
3, 8, 7, 2;
3, 11, 15, 9, 2;
...
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MAPLE
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if k < 0 or k > n then
0;
elif n = 0 then
1;
elif k=0 then
3;
elif k = n then
2;
else
procname(n-1, k-1)+procname(n-1, k) ;
end if;
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MATHEMATICA
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T[n_, k_]:= T[n, k]= If[n==0 && k==0, 1, If[k==0, 3, If[k==n, 2, T[n-1, k-1] + T[n-1, k] ]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 13 2019 *)
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PROG
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(PARI) T(n, k) = if(n==0 && k==0, 1, if(k==0, 3, if(k==n, 2, T(n-1, k-1) + T(n-1, k) ))); \\ G. C. Greubel, Nov 12 2019
(Sage)
@CachedFunction
def T(n, k):
if (n==0 and k==0): return 1
elif (k==0): return 3
elif (k==n): return 2
else: return T(n-1, k-1) + T(n-1, k)
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 12 2019
(GAP)
T:= function(n, k)
if n=0 and k=0 then return 1;
elif k=0 then return 3;
elif k=n then return 2;
else return T(n-1, k-1) + T(n-1, k);
fi;
end;
Flat(List([0..12], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Nov 12 2019
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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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