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A141431
Triangle T(n,k) = (k-1)*(3*n-k+1), read by rows.
1
0, 0, 5, 0, 8, 14, 0, 11, 20, 27, 0, 14, 26, 36, 44, 0, 17, 32, 45, 56, 65, 0, 20, 38, 54, 68, 80, 90, 0, 23, 44, 63, 80, 95, 108, 119, 0, 26, 50, 72, 92, 110, 126, 140, 152, 0, 29, 56, 81, 104, 125, 144, 161, 176, 189, 0, 32, 62, 90, 116, 140, 162, 182, 200, 216, 230, 0, 35, 68, 99, 128, 155, 180, 203, 224, 243, 260, 275
OFFSET
1,3
FORMULA
G.f.: Sum_{n>=0} Sum_{k>=0} T(n,k)*x^n*y^k = y^2*x*(x*y-4*y+x+2)/((1-y)^3*(1-x)^2). - R. J. Mathar, Nov 27 2015. x and y swapped to align with standard, 19 Feb 2020
Sum_{k=1..n} T(n, k) = (n-1)*n*(7*n+1)/6 = A245301(n-1). - G. C. Greubel, Mar 31 2021
EXAMPLE
Triangle begins as:
0;
0, 5;
0, 8, 14;
0, 11, 20, 27;
0, 14, 26, 36, 44;
0, 17, 32, 45, 56, 65;
0, 20, 38, 54, 68, 80, 90;
0, 23, 44, 63, 80, 95, 108, 119;
0, 26, 50, 72, 92, 110, 126, 140, 152;
0, 29, 56, 81, 104, 125, 144, 161, 176, 189;
MAPLE
A141431 := proc(n, k)
(k-1)*(3*n-k+1) ;
end proc:
seq(seq(A141431(n, k), k=1..n), n=1..14) ; # R. J. Mathar, Nov 10 2011
MATHEMATICA
Table[(k-1)*(3*n-k+1), {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Mar 31 2021 *)
PROG
(Magma) [(k-1)*(3*n-k+1): k in [1..n], n in [1..15]]; // G. C. Greubel, Mar 31 2021
(Sage) flatten([[(k-1)*(3*n-k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 31 2021
CROSSREFS
Columns: A016789 (k=2), A016933 (k=3), A008591 (k=4).
Cf. A245301 (row sums).
Sequence in context: A199729 A240358 A200422 * A166011 A344144 A372364
KEYWORD
nonn,easy,tabl
AUTHOR
EXTENSIONS
More terms added by G. C. Greubel, Mar 31 2021
STATUS
approved