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 A141402 Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows. 1
 0, 1, 1, 4, 8, 4, 9, 25, 25, 9, 16, 52, 80, 52, 16, 25, 89, 169, 169, 89, 25, 36, 136, 292, 360, 292, 136, 36, 49, 193, 449, 625, 625, 449, 193, 49, 64, 260, 640, 964, 1088, 964, 640, 260, 64, 81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81, 100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = n^2 + (2*k*(n-k))^2. Sum_{k=0..n} T(n, k) = n*(2*n^4 + 15*n^2 + 15*n -2)/15. - G. C. Greubel, Mar 30 2021 EXAMPLE Triangle begins as: 0; 1, 1; 4, 8, 4; 9, 25, 25, 9; 16, 52, 80, 52, 16; 25, 89, 169, 169, 89, 25; 36, 136, 292, 360, 292, 136, 36; 49, 193, 449, 625, 625, 449, 193, 49; 64, 260, 640, 964, 1088, 964, 640, 260, 64; 81, 337, 865, 1377, 1681, 1681, 1377, 865, 337, 81; 100, 424, 1124, 1864, 2404, 2600, 2404, 1864, 1124, 424, 100; MAPLE A141402:= (n, k)-> n^2 + (2*k*(n-k))^2; seq(seq(A141402(n, k), k=0..n), n=0..12); # G. C. Greubel, Mar 30 2021 MATHEMATICA T[n_, k_]:= n^2 + (2*k*(n-k))^2; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten PROG (Magma) [n^2 + (2*k*(n-k))^2: k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 30 2021 (Sage) flatten([[n^2 + (2*k*(n-k))^2 for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 30 2021 CROSSREFS Sequence in context: A165267 A092159 A322258 * A276619 A145900 A278676 Adjacent sequences: A141399 A141400 A141401 * A141403 A141404 A141405 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, Aug 03 2008 EXTENSIONS Edited by G. C. Greubel, Mar 30 2021 STATUS approved

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Last modified April 19 09:19 EDT 2024. Contains 371782 sequences. (Running on oeis4.)