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

1,3

LINKS

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

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 A266222

Adjacent sequences:  A141428 A141429 A141430 * A141432 A141433 A141434

KEYWORD

nonn,easy,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Aug 06 2008

EXTENSIONS

More terms added by G. C. Greubel, Mar 31 2021

STATUS

approved

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Last modified July 23 14:44 EDT 2021. Contains 346259 sequences. (Running on oeis4.)