reviewed

approved

proposed

reviewed

editing

proposed

Array read by antidiagonals: ((ceilceiling(sqrt(n)) + sqrt(n))^k + (ceilceiling(sqrt(n)) - sqrt(n))^k)/2 for columns k >= 0 and rows n >= 0.

For each row n >= 0 let T(n,0)=1 and T(n,1) =ceil 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

Cf. A191347 which uses floor() in place of ceilceiling().

approved

editing

reviewed

approved

proposed

reviewed

editing

proposed

Array read by antidiagonals: ((ceil(sqrt(xn)) + sqrt(x))^n))^k + (ceil(sqrt(xn)) - sqrt(x))^n))^k)/2 for all xcolumns k >= 0 and rows n >= 0.

For each row n>=0 let T(n,0)=1 and T(n,1)=ceil(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

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, ...

1, 2, 6, 20, 68, 232, 792, 2704, 9232, 31520, 107616, ...

1, 2, 7, 26, 97, 362, 1351, 5042, 18817, 70226, 262087, ...

1, 2, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288, ...

1, 3, 14, 72, 376, 1968, 10304, 53952, 282496, 1479168, 7745024, ...

1, 3, 15, 81, 441, 2403, 13095, 71361, 388881, 2119203, 11548575, ...

1, 3, 16, 90, 508, 2868, 16192, 91416, 516112, 2913840, 16450816, ...

1, 3, 17, 99, 577, 3363, 19601, 114243, 665857, 3880899, 22619537, ...

1, 3, 18, 108, 648, 3888, 23328, 139968, 839808, 5038848, 30233088, ...

1, 4, 26, 184, 1316, 9424, 67496, 483424, 3462416, 24798784, 177615776, ...

1, 4, 27, 196, 1433, 10484, 76707, 561236, 4106353, 30044644, 219825387, ...

1, 4, 28, 208, 1552, 11584, 86464, 645376, 4817152, 35955712, 268377088, ...

1, 4, 29, 220, 1673, 12724, 96773, 736012, 5597777, 42574180, 323800109, ...

1, 4, 30, 232, 1796, 13904, 107640, 833312, 6451216, 49943104, 386642400, ...

(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));

matrix(9, 9, n, k, T(n-1, k-1)) \\ Charles L. Hohn, Aug 23 2019

approved

editing

_Charles L. Hohn (ch+oeis(AT)1111-internet.com), _, May 31 2011

proposed

approved