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%I #14 Nov 17 2019 01:43:07
%S 1,0,1,0,1,1,0,2,2,1,0,4,6,2,1,0,8,20,7,2,1,0,16,68,26,8,3,1,0,32,232,
%T 97,32,14,3,1,0,64,792,362,128,72,15,3,1,0,128,2704,1351,512,376,81,
%U 16,3,1,0
%N Array read by antidiagonals: ((ceiling(sqrt(n)) + sqrt(n))^k + (ceiling(sqrt(n)) - sqrt(n))^k)/2 for columns k >= 0 and rows n >= 0.
%F For each row n >= 0 let T(n,0)=1 and T(n,1) = ceiling(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 23 2019
%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
%e 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...
%e 1, 2, 6, 20, 68, 232, 792, 2704, 9232, 31520, 107616, ...
%e 1, 2, 7, 26, 97, 362, 1351, 5042, 18817, 70226, 262087, ...
%e 1, 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288, ...
%e 1, 3, 14, 72, 376, 1968, 10304, 53952, 282496, 1479168, 7745024, ...
%e 1, 3, 15, 81, 441, 2403, 13095, 71361, 388881, 2119203, 11548575, ...
%e 1, 3, 16, 90, 508, 2868, 16192, 91416, 516112, 2913840, 16450816, ...
%e 1, 3, 17, 99, 577, 3363, 19601, 114243, 665857, 3880899, 22619537, ...
%e 1, 3, 18, 108, 648, 3888, 23328, 139968, 839808, 5038848, 30233088, ...
%e 1, 4, 26, 184, 1316, 9424, 67496, 483424, 3462416, 24798784, 177615776, ...
%e 1, 4, 27, 196, 1433, 10484, 76707, 561236, 4106353, 30044644, 219825387, ...
%e 1, 4, 28, 208, 1552, 11584, 86464, 645376, 4817152, 35955712, 268377088, ...
%e 1, 4, 29, 220, 1673, 12724, 96773, 736012, 5597777, 42574180, 323800109, ...
%e 1, 4, 30, 232, 1796, 13904, 107640, 833312, 6451216, 49943104, 386642400, ...
%e ...
%o (PARI) T(n, k) = if (k==0, 1, if (k==1, ceil(sqrt(n)), T(n,k-2)*(n-T(n,1)^2) + T(n,k-1)*T(n,1)*2));
%o matrix(9, 9, n, k, T(n-1, k-1)) \\ _Charles L. Hohn_, Aug 23 2019
%Y Row 1 is A000007, row 2 is A011782, row 3 is A006012, row 4 is A001075, row 5 is A081294, row 6 is A098648, row 7 is A084120, row 8 is A146963, row 9 is A001541, row 10 is A081341, row 11 is A084134, row 13 is A090965.
%Y Row 3*2 is A056236, row 4*2 is A003500, row 5*2 is A155543, row 9*2 is A003499.
%Y Cf. A191347 which uses floor() in place of ceiling().
%K nonn,tabl
%O 0,8
%A _Charles L. Hohn_, May 31 2011