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A119687 f-Pascal's triangle where f(n) = n^2 = A000290(n). 3
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The second diagonal, T(n,n-1) = A003095(n). - Cortney Reagle, Sep 17 2019

LINKS

Cortney Reagle, Table of n, a(n) for n = 0..104 (Rows n=0..12 of triangle, flattened)

FORMULA

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.

EXAMPLE

Triangle begins:

  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;

  ...

PROG

(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

CROSSREFS

Row sums are A327563.

Cf. A007318, A003095.

Sequence in context: A060854 A091378 A156045 * A086856 A052916 A326048

Adjacent sequences:  A119684 A119685 A119686 * A119688 A119689 A119690

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Jun 09 2006

EXTENSIONS

a(12) = 50 inserted and more terms added by Cortney Reagle, Sep 17 2019

STATUS

approved

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Last modified February 19 04:00 EST 2020. Contains 332034 sequences. (Running on oeis4.)