A060494 a(n) = floor(n^4/64).
0, 0, 0, 1, 4, 9, 20, 37, 64, 102, 156, 228, 324, 446, 600, 791, 1024, 1305, 1640, 2036, 2500, 3038, 3660, 4372, 5184, 6103, 7140, 8303, 9604, 11051, 12656, 14430, 16384, 18530, 20880, 23447, 26244, 29283, 32580, 36147, 40000, 44152, 48620, 53418, 58564, 64072
Offset: 0
Examples
a(9) = floor(9^4/64) = floor(6561/64) = floor(102.51562...) = 102.
Links
- Harry J. Smith, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -4, 6, -4, 1).
Programs
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Mathematica
Floor[Range[0,50]^4/64] (* or *) LinearRecurrence[ {4,-6,4,-1,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1},{0,0,0,1,4,9,20,37,64,102,156,228,324,446,600,791,1024,1305,1640,2036},50] (* Harvey P. Dale, May 30 2014 *) -
PARI
a(n) = { n^4\64 } \\ Harry J. Smith, Jul 06 2009
Formula
a(n) = floor(A000583(n)/64) = floor(A011863(n-1)/4). a(2n) = A059403(2n); a(2n-1) = A059403(2n-1) + A011861(n).
From R. J. Mathar, Mar 24 2011: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-16) - 4*a(n-17) + 6*a(n-18) - 4*a(n-19) + a(n-20).
G.f.: -x^3 *(1 - x^2 + 4*x^3 - 4*x^4 - 3*x^6 + 4*x^7 - 3*x^8 + 4*x^9 - 4*x^10 + 4*x^11 - x^12 + x^14 + 4*x^5) / ( (1+x) *(x^2+1) *(x^4+1) *(x^8+1) *(x-1)^5 ). (End)