A163989 First differences of A160379.
1, 26, 8, 200, 26, 620, 56, 1304, 98, 2252, 152, 3464, 218, 4940, 296, 6680, 386, 8684, 488, 10952, 602, 13484, 728, 16280, 866, 19340, 1016, 22664, 1178, 26252, 1352, 30104, 1538, 34220, 1736, 38600, 1946, 43244, 2168, 48152, 2402, 53324, 2648, 58760, 2906
Offset: 1
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
- Index entries for sequences related to cellular automata
- Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).
Programs
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Mathematica
LinearRecurrence[{0,3,0,-3,0,1},{1,26,8,200,26,620,56,1304},50] (* Harvey P. Dale, May 19 2025 *) -
PARI
Vec(-x*(18*x^3+x^2+26*x+1)*(x^4+4*x^2+1)/((x-1)^3*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 17 2013
Formula
a(2n+1) = 6n^2 + 2 for n>=1.
a(2n) = 132n^2 - 240n + 152 for n>=2.
From Colin Barker, Sep 17 2013: (Start)
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6) for n>8.
G.f.: -x*(18*x^3+x^2+26*x+1)*(x^4+4*x^2+1) / ((x-1)^3*(x+1)^3). (End)
Extensions
Formula and more terms from Nathaniel Johnston, Nov 15 2010
More terms from Colin Barker, Sep 17 2013