The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173567 Triangle T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = (1/2)*Sum_{j=1..2*n} k^j, read by rows. 1
 2, 5, 5, 9, 30, 9, 14, 123, 123, 14, 20, 425, 1092, 425, 20, 27, 1413, 7650, 7650, 1413, 27, 35, 4872, 54051, 87380, 54051, 4872, 35, 44, 17783, 426573, 943190, 943190, 426573, 17783, 44, 54, 67875, 3655854, 12192579, 12207030, 12192579, 3655854, 67875, 54 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Rows n = 1..50 of the triangle, flattened FORMULA T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = (1/2)*Sum_{j=1..2*n} k^j. T(n, k) = (f(k, n-k+1) + f(n-k+1, k))/2 where f(n, k) = k*(1 - k^(2*n))/(1-k) with f(n, 1) = 2*n. - G. C. Greubel, Apr 25 2021 EXAMPLE Triangle begins as: 2; 5, 5; 9, 30, 9; 14, 123, 123, 14; 20, 425, 1092, 425, 20; 27, 1413, 7650, 7650, 1413, 27; 35, 4872, 54051, 87380, 54051, 4872, 35; 44, 17783, 426573, 943190, 943190, 426573, 17783, 44; 54, 67875, 3655854, 12192579, 12207030, 12192579, 3655854, 67875, 54; MATHEMATICA f[n_, k_]:= If[k==1, 2*n, k*(1-k^(2*n))/(1-k)]; T[n_, k_]:= (f[k, n-k+1] + f[n-k+1, k])/2; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Apr 25 2021 *) PROG (Sage) def f(n, k): return 2*n if k==1 else k*(1-k^(2*n))/(1-k) def T(n, k): return (f(k, n-k+1) + f(n-k+1, k))/2 flatten([[T(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Apr 25 2021 CROSSREFS Sequence in context: A050175 A243333 A059797 * A288726 A344572 A265129 Adjacent sequences: A173564 A173565 A173566 * A173568 A173569 A173570 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 22 2010 EXTENSIONS Edited by G. C. Greubel, Apr 25 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 11:09 EST 2022. Contains 358493 sequences. (Running on oeis4.)