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First term of n-th difference sequence of (floor(k*r)), r = 1/2 + sqrt(2), k >= 0.
2

%I #16 Jul 20 2019 22:20:25

%S 1,1,-1,1,-1,1,-1,1,-1,1,-1,0,11,-77,363,-1364,4367,-12375,31823,

%T -75581,167959,-352715,705431,-1352078,2496167,-4457699,7728759,

%U -13055444,21572459,-35072309,56663099,-92561039,157073279,-286097759,572195518,-1251677664

%N First term of n-th difference sequence of (floor(k*r)), r = 1/2 + sqrt(2), k >= 0.

%H Clark Kimberling, <a href="/A325733/b325733.txt">Table of n, a(n) for n = 1..200</a>

%t Table[First[Differences[Table[Floor[(1/2+Sqrt[2])*n], {n, 0, 50}], n]], {n, 1, 50}]

%Y Cf. A325664. Inverse binomial transform of A137803.

%K easy,sign

%O 1,13

%A _Clark Kimberling_, May 20 2019