A309853 Array read by antidiagonals: ((z+sqrt(x))/2)^k + ((z-sqrt(x))/2)^k for columns k >= 0 and rows n >= 0, where x = 4*n+1 and y = ceiling(sqrt(x)) and z = y+1-(y mod 2).
2, 1, 2, 1, 3, 2, 1, 7, 3, 2, 1, 18, 9, 5, 2, 1, 47, 27, 19, 5, 2, 1, 123, 81, 80, 21, 5, 2, 1, 322, 243, 343, 95, 23, 5, 2, 1, 843, 729, 1475, 433, 110, 25, 7, 2, 1, 2207, 2187, 6346, 1975, 527, 125, 39, 7, 2, 1, 5778, 6561, 27305, 9009, 2525, 625, 238, 41, 7, 2
Offset: 0
Examples
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... 2, 3, 7, 18, 47, 123, 322, 843, 2207, 5778, ... 2, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, ... 2, 5, 19, 80, 343, 1475, 6346, 27305, 117487, 505520, ... 2, 5, 21, 95, 433, 1975, 9009, 41095, 187457, 855095, ... 2, 5, 23, 110, 527, 2525, 12098, 57965, 277727, 1330670, ... 2, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, ... 2, 7, 39, 238, 1471, 9107, 56394, 349223, 2162591, 13392022, ... 2, 7, 41, 259, 1649, 10507, 66953, 426643, 2718689, 17324251, ... 2, 7, 43, 280, 1831, 11977, 78346, 512491, 3352399, 21929320, ... 2, 7, 45, 301, 2017, 13517, 90585, 607061, 4068257, 27263677, ... ...
Crossrefs
Programs
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PARI
T(n, k) = my(x = 4*n+1, y = ceil(sqrt(x)), z = y+1-(y % 2)); round(((z+sqrt(x))/2)^k + ((z-sqrt(x))/2)^k); matrix(9, 9, n, k, T(n-1, k-1)) \\ Michel Marcus, Aug 22 2019
Extensions
Revised orientation of n and k to customary T(n, k), by Charles L. Hohn, Sep 27 2024
Comments