A094930 Triangle T(n,m) read by rows, defined by squaring a matrix with row entries 2+3*(m-1).

4, 14, 25, 30, 65, 64, 52, 120, 152, 121, 80, 190, 264, 275, 196, 114, 275, 400, 462, 434, 289, 154, 375, 560, 682, 714, 629, 400, 200, 490, 744, 935, 1036, 1020, 860, 529, 252, 620, 952, 1221, 1400, 1462, 1380, 1127, 676, 310, 765, 1184, 1540, 1806, 1955, 1960

Offset

1,1

Comments

Matrix square of the matrix B(n,m) = 2+3*(m-1), B containing the first terms of A016789

in its row n, n>0, 1<=m<=n.

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

Formula

T(n,m) = sum_{k=m..n} B(n,k)*B(k,m) = (3*m-1)*(3*m+3*n-2)*(n+1-m)/2.

Row sums: sum_{m=1..n} T(n,m) = A024212(n).

G.f. as triangle: x*y*(4+2*x+13*x*y-16*x^2*y+x^2*y^2-4*x^3*y^2)/((1-x)*(1-x*y))^3. - Robert Israel, May 06 2019

Example

The matrix B starts as
  2 ;
  2,5 ;
  2,5,8 ;
  2,5,8,11 ;
  2,5,8,11,14 ;
and interpreting this as a lower triangular matrix, its square T = B^2 starts
  4;
  14,25;
  30,65,64;
  52,120,152,121;

Maple

A094930 := proc(n, m) (3*m-1)*(3*m+3*n-2)*(n+1-m)/2 ; end: seq(seq(A094930(n, m), m=1..n), n=1..20) ; # R. J. Mathar, Oct 09 2009

Crossrefs

Cf. A024212, A096037, A011379, A002411, A096038, A095794.

Sequence in context: A017317 A195973 A116963 * A289665 A080286 A075381

Adjacent sequences: A094927 A094928 A094929 * A094931 A094932 A094933

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Jun 17 2004

Extensions

Edited and extended by R. J. Mathar, Oct 09 2009

Status

approved