A062707 Table by antidiagonals of n*k*(k+1)/2.

0, 0, 0, 0, 1, 0, 0, 3, 2, 0, 0, 6, 6, 3, 0, 0, 10, 12, 9, 4, 0, 0, 15, 20, 18, 12, 5, 0, 0, 21, 30, 30, 24, 15, 6, 0, 0, 28, 42, 45, 40, 30, 18, 7, 0, 0, 36, 56, 63, 60, 50, 36, 21, 8, 0, 0, 45, 72, 84, 84, 75, 60, 42, 24, 9, 0, 0, 55, 90, 108, 112, 105, 90, 70, 48, 27, 10, 0

Offset: 0

Author

Henry Bottomley, Jul 11 2001

Keywords

• easy
• nonn
• tabl

Examples

			  0   0   0   0   0   0   0   0   0
  0   1   3   6  10  15  21  28  36
  0   2   6  12  20  30  42  56  72
  0   3   9  18  30  45  63  84 108
  0   4  12  24  40  60  84 112 144
  0   5  15  30  50  75 105 140 180
  0   6  18  36  60  90 126 168 216
  0   7  21  42  70 105 147 196 252
  0   8  24  48  80 120 168 224 288
		

Links

• G. C. Greubel, Antidiagonals n = 0..100, flattened

Crossrefs

Main diagonal is A002411. Sum of antidiagonals is A000332.

Programs

GAP

Flat(List([0..12], n-> List([0..n], k-> k*Binomial(n-k+1,2)))); # G. C. Greubel, Sep 02 2019

Magma

[k*Binomial(n-k+1,2): k in [0..n], n in [0..12]]; // G. C. Greubel, Sep 02 2019

Maple

seq(seq(k*binomial(n-k+1,2), k=0..n), n=0..12); # G. C. Greubel, Sep 02 2019

Mathematica

Table[k*Binomial[n-k+1, 2], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Sep 02 2019 *)

PARI

T(n,k) = k*binomial(n-k+1,2);
for(n=0,12, for(k=0,n, print1(T(n,k), ", "))) \\ G. C. Greubel, Sep 02 2019

Sage

[[k*binomial(n-k+1,2) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Sep 02 2019

Formula

T(n, k) = T(n, 1)*T(1, k) = A001477(n)*A000217(k).

T(n, k) = A057145(n+2, k+1)-(k+1).