A143844 Triangle T(n,k) = k^2 read by rows.

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

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

Table of n, a(n) for n=0..77.

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

Cf. A000290, A002262, A002415, A002674, A040977, A053347, A054334, A133819.

Sequence in context: A299528 A300146 A100045 * A186759 A065623 A178103

Adjacent sequences: A143841 A143842 A143843 * A143845 A143846 A143847

Keyword

nonn,tabl,easy

Author

Paul Curtz, Sep 03 2008

Extensions

Definition simplified by R. J. Mathar, Sep 07 2009

Status

approved