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A143844 Triangle T(n,k) = k^2 read by rows. 1
0, 0, 1, 0, 1, 4, 0, 1, 4, 9, 0, 1, 4, 9, 16, 0, 1, 4, 9, 16, 25, 0, 1, 4, 9, 16, 25, 36, 0, 1, 4, 9, 16, 25, 36, 49, 0, 1, 4, 9, 16, 25, 36, 49, 64, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
This is triangle A133819 with an additional leading column of zeros.
There is a family of even integer-valued polynomials p_n(x) = product_{k=0..n} (x^2 - T(n,k))/ A002674(n+1). We find p_0(x) in A000290, p_1(x) in A002415, p_2(x) essentially in A040977, p_3(x) in A053347 and p_4(x) in A054334. - Paul Curtz, Jun 10 2011
LINKS
FORMULA
T(n,k) = (A002262(n,k))^2.
G.f.: x*y*(1 + x*y)/((1 - x)*(1 - x*y)^3). - Stefano Spezia, Feb 21 2024
MATHEMATICA
Table[Range[0, n]^2, {n, 0, 15}]//Flatten (* Harvey P. Dale, Sep 08 2017 *)
PROG
(PARI) for(n=0, 9, for(k=0, n, print1(k^2", "))) \\ Charles R Greathouse IV, Jun 10 2011
CROSSREFS
Sequence in context: A299528 A300146 A100045 * A186759 A065623 A178103
KEYWORD
nonn,tabl,easy
AUTHOR
Paul Curtz, Sep 03 2008
EXTENSIONS
Definition simplified by R. J. Mathar, Sep 07 2009
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)