A062707 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,8

LINKS

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

FORMULA

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

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

EXAMPLE

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

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 *)

PROG

(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

(Magma) [k*Binomial(n-k+1, 2): k in [0..n], n in [0..12]]; // 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

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

CROSSREFS

Main diagonal is A002411. Sum of antidiagonals is A000332.

Sequence in context: A062787 A131370 A261180 * A160230 A373418 A293500

Adjacent sequences: A062704 A062705 A062706 * A062708 A062709 A062710

KEYWORD

easy,nonn,tabl

AUTHOR

Henry Bottomley, Jul 11 2001

STATUS

approved