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 A127159 Triangle T(n,k) with T(n,k) = A061554(n,k) + A107430(n,k). 1
 2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 7, 5, 8, 5, 7, 11, 11, 10, 10, 11, 11, 21, 16, 21, 12, 21, 16, 21, 36, 36, 28, 28, 28, 28, 36, 36, 71, 57, 64, 36, 56, 36, 64, 57, 71, 127, 127, 93, 93, 72, 72, 93, 93, 127, 127, 253, 211, 220, 130, 165, 90, 165, 130, 220, 211, 253 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Rows n = 0..100 of triangle, flattened FORMULA Sum_{k=0..n} T(n,k) = 2^(n+1). T(n, k) = binomial(n, floor((n+1 - (-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)). - G. C. Greubel, Jan 31 2020 EXAMPLE Triangle begins: 2; 2, 2; 3, 2, 3; 4, 4, 4, 4; 7, 5, 8, 5, 7; 11, 11, 10, 10, 11, 11; 21, 16, 21, 12, 21, 16, 21; 36, 36, 28, 28, 28, 28, 36, 36; 71, 57, 64, 36, 56, 36, 64, 57, 71; ... MAPLE seq(seq( binomial(n, floor((n+1-(-1)^(n-k)*(k+1))/2)) +binomial(n, floor(k/2)), k=0..n), n=0..12); # G. C. Greubel, Jan 31 2020 MATHEMATICA T[n_, k_]= Binomial[n, Floor[(n+1 -(-1)^(n-k)*(k+1))/2]] + Binomial[n, Floor[k/2]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jan 31 2020 *) PROG (PARI) T(n, k) = binomial(n, (n+1 -(-1)^(n-k)*(k+1))\2 ) + binomial(n, k\2); \\ G. C. Greubel, Jan 31 2020 (Magma) [Binomial(n, Floor((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Floor(k/2)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 31 2020 (Sage) [[binomial(n, floor((n+1 -(-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 31 2020 (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, Int((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Int(k/2)) ))); # G. C. Greubel, Jan 31 2020 CROSSREFS Cf. A061554, A107430. Sequence in context: A143976 A194296 A194336 * A025128 A058769 A194312 Adjacent sequences: A127156 A127157 A127158 * A127160 A127161 A127162 KEYWORD nonn,tabl AUTHOR Philippe Deléham, Mar 25 2007 STATUS approved

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Last modified April 1 12:16 EDT 2023. Contains 361691 sequences. (Running on oeis4.)