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 A191347 Array read by antidiagonals: ((floor(sqrt(n)) + sqrt(n))^k + (floor(sqrt(n)) - sqrt(n))^k)/2 for columns k >= 0 and rows n >= 0. 3
 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 4, 3, 1, 1, 0, 8, 7, 4, 2, 1, 0, 16, 17, 10, 8, 2, 1, 0, 32, 41, 28, 32, 9, 2, 1, 0, 64, 99, 76, 128, 38, 10, 2, 1, 0, 128, 239, 208, 512, 161, 44, 11, 2, 1, 0, 256, 577, 568, 2048, 682, 196, 50, 12, 3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS FORMULA For each row n>=0 let T(n,0)=1 and T(n,1)=floor(sqrt(n)), then for each column k>=2: T(n,k)=T(n,k-2)*(n-T(n,1)^2) + T(n,k-1)*T(n,1)*2. - Charles L. Hohn, Aug 22 2019 T(n, k) = Sum_(i=0, floor((k+1)/2), binomial(k, 2*i)*floor(sqrtint(n))^(k-2*i)*n^i)) for n > 0, with T(0, 0) = 1 and T(0, k) = 0 for k > 0. - Michel Marcus, Aug 23 2019 EXAMPLE 1, 0,  0,   0,    0,    0,     0,      0,       0,        0,        0, ... 1, 1,  2,   4,    8,   16,    32,     64,     128,      256,      512, ... 1, 1,  3,   7,   17,   41,    99,    239,     577,     1393,     3363, ... 1, 1,  4,  10,   28,   76,   208,    568,    1552,     4240,    11584, ... 1, 2,  8,  32,  128,  512,  2048,   8192,   32768,   131072,   524288, ... 1, 2,  9,  38,  161,  682,  2889,  12238,   51841,   219602,   930249, ... 1, 2, 10,  44,  196,  872,  3880,  17264,   76816,   341792,  1520800, ... 1, 2, 11,  50,  233, 1082,  5027,  23354,  108497,   504050,  2341691, ... 1, 2, 12,  56,  272, 1312,  6336,  30592,  147712,   713216,  3443712, ... 1, 3, 18, 108,  648, 3888, 23328, 139968,  839808,  5038848, 30233088, ... 1, 3, 19, 117,  721, 4443, 27379, 168717, 1039681,  6406803, 39480499, ... 1, 3, 20, 126,  796, 5028, 31760, 200616, 1267216,  8004528, 50561600, ... 1, 3, 21, 135,  873, 5643, 36477, 235791, 1524177,  9852435, 63687141, ... 1, 3, 22, 144,  952, 6288, 41536, 274368, 1812352, 11971584, 79078912, ... 1, 3, 23, 153, 1033, 6963, 46943, 316473, 2133553, 14383683, 96969863, ... ... PROG (PARI) T(n, k) = if (n==0, k==0, my(x=sqrtint(n)); sum(i=0, (k+1)\2, binomial(k, 2*i)*x^(k-2*i)*n^i)); matrix(9, 9, n, k, T(n-1, k-1)) \\ Michel Marcus, Aug 22 2019 (PARI) T(n, k) = if (k==0, 1, if (k==1, sqrtint(n), T(n, k-2)*(n-T(n, 1)^2) + T(n, k-1)*T(n, 1)*2)); matrix(9, 9, n, k, T(n-1, k-1)) \\ Charles L. Hohn, Aug 22 2019 CROSSREFS Row 1 is A000007, row 2 is A011782, row 3 is A001333, row 4 is A026150, row 5 is A081294, row 6 is A001077, row 7 is A084059, row 8 is A108851, row 9 is A084128, row 10 is A081341, row 11 is A005667, row 13 is A141041. Row 3*2 is A002203, row 4*2 is A080040, row 5*2 is A155543, row 6*2 is A014448, row 8*2 is A080042, row 9*2 is A170931, row 11*2 is A085447. Cf. A191348 which uses ceiling() in place of floor(). Sequence in context: A318686 A214546 A255704 * A106234 A238125 A062507 Adjacent sequences:  A191344 A191345 A191346 * A191348 A191349 A191350 KEYWORD nonn,tabl AUTHOR Charles L. Hohn, May 31 2011 STATUS approved

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)