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 A131240 T(n,k) = 2*A046854(n,k) - I. 2
 1, 2, 1, 2, 2, 1, 2, 4, 2, 1, 2, 4, 6, 2, 1, 2, 6, 6, 8, 2, 1, 2, 6, 12, 8, 10, 2, 1, 2, 8, 12, 20, 10, 12, 2, 1, 2, 8, 20, 20, 30, 12, 14, 2, 1, 2, 10, 20, 40, 30, 42, 14, 16, 2, 1, 2, 10, 30, 40, 70, 42, 56, 16, 18, 2, 1, 2, 12, 30, 70, 70, 112, 56, 72, 18, 20, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums = A001595: (1, 3, 5, 9, 15, 25, 41, 67, ...). A131241 = 3*A046854 - 2*I. LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA T(n,k) = 2*A046854(n,k) - Identity matrix, where A046854 = Pascal's triangle with repeats by columns. EXAMPLE First few rows of the triangle: 1; 2, 1; 2, 2, 1; 2, 4, 2, 1; 2, 4, 6, 2, 1; 2, 6, 6, 8, 2, 1; 2, 6, 12, 8, 10, 2, 1; ... MATHEMATICA Table[If[k==n, 1, 2*Binomial[Floor[(n+k)/2], k]], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 12 2019 *) PROG (PARI) T(n, k) = if(k==n, 1, 2*binomial((n+k)\2, k)); (Magma) [k eq n select 1 else 2*Binomial(Floor((n+k)/2), k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 12 2019 (Sage) def T(n, k): if (k==n): return 1 else: return 2*binomial(floor((n+k)/2), k) [[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 12 2019 (GAP) T:= function(n, k) if k=n then return 1; else return 2*Binomial(Int((n+k)/2), k); fi; end; Flat(List([0..12], n-> List([0..n], k-> T(n, k)))); # G. C. Greubel, Jul 12 2019 CROSSREFS Cf. A001595, A046854, A131241. Sequence in context: A078498 A350700 A178522 * A263666 A107027 A355395 Adjacent sequences: A131237 A131238 A131239 * A131241 A131242 A131243 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jun 21 2007 EXTENSIONS More terms added by G. C. Greubel, Jul 12 2019 STATUS approved

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Last modified June 8 03:07 EDT 2023. Contains 363157 sequences. (Running on oeis4.)