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 A171824 Triangle T(n,k)= binomial(n + k,n) + binomial(2*n-k,n) read by rows. 1
 2, 3, 3, 7, 6, 7, 21, 14, 14, 21, 71, 40, 30, 40, 71, 253, 132, 77, 77, 132, 253, 925, 469, 238, 168, 238, 469, 925, 3433, 1724, 828, 450, 450, 828, 1724, 3433, 12871, 6444, 3048, 1452, 990, 1452, 3048, 6444, 12871, 48621, 24320, 11495, 5225, 2717, 2717, 5225, 11495, 24320, 48621 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1325 FORMULA T(n,k) = A046899(n,k) + A092392(n,k). Sum_{k=0..n} T(n,k) = binomial(2*n+2, n+1) = 2*A001700(n) = A000984(n+1). - G. C. Greubel, Apr 29 2021 EXAMPLE Triangle begins as:        2;        3,     3;        7,     6,     7;       21,    14,    14,    21;       71,    40,    30,    40,   71;      253,   132,    77,    77,  132,  253;      925,   469,   238,   168,  238,  469, 925;     3433,  1724,   828,   450,  450,  828, 1724,  3433;    12871,  6444,  3048,  1452,  990, 1452, 3048,  6444, 12871;    48621, 24320, 11495,  5225, 2717, 2717, 5225, 11495, 24320, 48621;   184757, 92389, 43824, 19734, 9009, 6006, 9009, 19734, 43824, 92389, 184757; MATHEMATICA T[n_, k_] = Binomial[n+k, k] + Binomial[2*n-k, n-k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten PROG (Magma) T:= func< n, k | Binomial(n+k, n) + Binomial(2*n-k, n) >; [T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 29 2021 (Sage) def T(n, k): return binomial(n+k, n) + binomial(2*n-k, n) flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 29 2021 CROSSREFS Row sums are A000984(n+1). Cf. A001700, A007318, A054142, A085478. Sequence in context: A253357 A185909 A193713 * A143444 A108346 A210558 Adjacent sequences:  A171821 A171822 A171823 * A171825 A171826 A171827 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula, Dec 19 2009 EXTENSIONS Formula and row sums reference added by the Assoc. Editors of the OEIS, Feb 24 2010 STATUS approved

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Last modified June 21 03:24 EDT 2021. Contains 345354 sequences. (Running on oeis4.)