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 A176348 Triangle, read by rows: T(n, k) = binomial(n, k)*(1 + 2*(n+1) - (k+1)*floor((n+1)/(k+1)) - (n-k+1)* floor((n+1)/(n-k+1))). 1
 1, 1, 1, 1, 6, 1, 1, 6, 6, 1, 1, 12, 30, 12, 1, 1, 10, 30, 30, 10, 1, 1, 18, 60, 140, 60, 18, 1, 1, 14, 105, 140, 140, 105, 14, 1, 1, 24, 84, 280, 630, 280, 84, 24, 1, 1, 18, 144, 504, 630, 630, 504, 144, 18, 1, 1, 30, 225, 840, 1260, 2772, 1260, 840, 225, 30, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 8, 14, 56, 82, 298, 520, 1408, 2594, 7484, ...}. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n, k) = binomial(n, k)*(1 +2*(n+1) -(k+1)*floor((n+1)/(k+1)) -(n-k+1)* floor((n+1)/(n-k+1))). EXAMPLE Triangle begins as: 1; 1, 1; 1, 6, 1; 1, 6, 6, 1; 1, 12, 30, 12, 1; 1, 10, 30, 30, 10, 1; 1, 18, 60, 140, 60, 18, 1; 1, 14, 105, 140, 140, 105, 14, 1; 1, 24, 84, 280, 630, 280, 84, 24, 1; 1, 18, 144, 504, 630, 630, 504, 144, 18, 1; 1, 30, 225, 840, 1260, 2772, 1260, 840, 225, 30, 1; MAPLE T:=binomial(n, k)*(2*n+3 -(k+1)*floor((n+1)/(k+1)) -(n-k+1)* floor((n+1)/(n-k+1))); seq(seq(T(n, k), k=0..n), n=0..12); # G. C. Greubel, Nov 23 2019 MATHEMATICA T[n_, k_]:= T[n, k]= Binomial[n, k]*(2*n+3 -(k+1)*Floor[(n+1)/(k+1)] -(n - k+1)*Floor[(n+1)/(n-k+1)]); Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten PROG (PARI) T(n, k) = binomial(n, k)*(2*n+3 -(k+1)*((n+1)\(k+1)) -(n-k+1)* ((n+1)\(n-k+1))); \\ G. C. Greubel, Nov 23 2019 (Magma) [Binomial(n, k)*(2*n+3 -(k+1)*Floor((n+1)/(k+1)) -(n-k+1)* Floor((n+1)/(n-k+1))): k in [0..n], n in [0..12]]; // G. C. Greubel, Nov 23 2019 (Sage) [[binomial(n, k)*(2*n+3 -(k+1)*floor((n+1)/(k+1)) -(n-k+1)* floor((n+1)/(n-k+1))) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Nov 23 2019 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, k)*(2*n+3 -(k+1)*Int((n+1)/(k+1)) -(n-k+1)*Int((n+1)/(n-k+1))) ))); # G. C. Greubel, Nov 23 2019 CROSSREFS Cf. A007318, A176298. Sequence in context: A131778 A095713 A138072 * A176264 A195397 A173741 Adjacent sequences: A176345 A176346 A176347 * A176349 A176350 A176351 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Apr 15 2010 EXTENSIONS Edited by G. C. Greubel, Nov 23 2019 STATUS approved

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Last modified June 8 07:54 EDT 2023. Contains 363157 sequences. (Running on oeis4.)