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A119687
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f-Pascal's triangle where f(n) = n^2 = A000290(n).
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3
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1, 1, 1, 1, 2, 1, 1, 5, 5, 1, 1, 26, 50, 26, 1, 1, 677, 3176, 3176, 677, 1, 1, 458330, 10545305, 20173952, 10545305, 458330, 1, 1, 210066388901, 111413523931925, 518191796841329, 518191796841329, 111413523931925, 210066388901, 1
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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T(n, k) = T(n-1, k-1)^2 + T(n-1, k)^2; T(0,0) = 1; T(n,-1) = 0; T(n, k) = 0, n < k.
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EXAMPLE
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Triangle T(n,k) (with rows n >= 0 and columns 0 <= k <= n) begins as follows:
1;
1, 1;
1, 2, 1;
1, 5, 5, 1;
1, 26, 50, 26, 1;
1, 677, 3176, 3176, 677, 1;
1, 458330, 10545305, 20173952, 10545305, 458330, 1;
...
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PROG
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(PARI) T(n)={my(M=matrix(n, n)); M[1, 1]=1; for(n=2, n, M[n, 1]=1; for(k=2, n, M[n, k]=M[n-1, k-1]^2 + M[n-1, k]^2)); M}
{ my(A=T(7)); for(i=1, #A, print(A[i, 1..i])) } \\ Andrew Howroyd, Sep 17 2019
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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a(12) = 50 inserted and more terms added by Cortney Reagle, Sep 17 2019
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STATUS
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approved
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