1,2

Or, triangle read by rows, in which row n gives the numbers n*1, (n-1)*2, (n-2)*3, ..., 2*(n-1), 1*n.

Radius of incircle of Pythagorean triangle with sides a=(n+1)^2-m^2, b=2*(n+1)*m and c=(n+1)^2+m^2. - Floor van Lamoen (fvlamoen(AT)hotmail.com), Aug 16 2001

A permutation of A061017. - Matthew Vandermast (ghodges14(AT)comcast.net), Feb 28 2003

In the proof of countability of rational numbers they are arranged in a square array. a(n) = p*q where p/q is the corresponding rational number as read from the array. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), May 29 2003

Permanent of upper right n X n corner is A000442. - Marc LeBrun (mlb(AT)well.com), Dec 11 2003

Row 12 gives total number of partridges, turtle doves, ... and drummers drumming that you have received at the end of the Twelve Days of Christmas song. - Alonso Del Arte, Jun 17 2005

Generated by additive equivalent of binomial theorem : T(i,j) = t(i)-t(j)-t(i-j), where t(k)=k(k+1)/2 - Jon Perry (perry(AT)globalnet.co.uk), Nov 23 2005

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 46.

T. D. Noe, Table of n, a(n) for n=1..5050

A. Necer, Series formelles et produit de Hadamard

T(n, m)=m*(n-m+1).

Sum i=1..n Sum j=1..n a(n) = A000537(n) [Sum of first n cubes; or n-th triangular number squared.] Determinant of all n X n contiguous subarrays of A003991 is 0. - Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Sep 26 2004

G.f.: x * y / [ (1-x)^2 * (1-y)^2 ].

a(n)=(i-j+1)*j, where i=floor((1+sqr(8n-7))/2), j=n-i*(i-1)/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 08 2007

As an infinite lower triangular matrix equals A000012 * A002260; where A000012 = (1; 1,1; 1,1,1;...) and A002260 = (1; 1,2; 1,2,3;...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 23 2007

t(n,m)=n/(1/m + 1/(n - m)) [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009]

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009: (Start)

{1},

{2, 2},

{3, 4, 3},

{4, 6, 6, 4},

{5, 8, 9, 8, 5},

{6, 10, 12, 12, 10, 6},

{7, 12, 15, 16, 15, 12, 7},

{8, 14, 18, 20, 20, 18, 14, 8},

{9, 16, 21, 24, 25, 24, 21, 16, 9},

{10, 18, 24, 28, 30, 30, 28, 24, 18, 10},

{11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11},

{12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12},

{13, 24, 33, 40, 45, 48, 49, 48, 45, 40, 33, 24, 13} (End)

Table[(x + 1 - y) y, {x, 13}, {y, x}] // Flatten (* Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 06 2007 *)

Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 02 2009: (Start)

Clear[f]; f[n_, m_] = n/(1/m + 1/(n - m));

Table[Table[f[n, m], {m, 1, n - 1}], {n, 2, 14}];

Flatten[%] (End)

(PARI) T(n, k) = if(k<1|k>n, 0, k*(n+1-k))

Main diagonal gives squares A000290. Anti-diagonal sums are tetrahedral numbers A000292. See A004247 for another version.

Cf. A003989, A003990, A003056, A049581, A000442, A027424.

Cf. A002260.

Adjacent sequences: A003988 A003989 A003990 this_sequence A003992 A003993 A003994

Sequence in context: A162619 A032355 A091257 this_sequence A131923 A119457 A065157

tabl,nonn,nice,easy

Marc LeBrun (mlb(AT)well.com)

More terms from Michael Somos