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A212668
a(n) = (16/3)*(n+1)*n*(n-1) + 8*n^2 + 1.
6
9, 65, 201, 449, 841, 1409, 2185, 3201, 4489, 6081, 8009, 10305, 13001, 16129, 19721, 23809, 28425, 33601, 39369, 45761, 52809, 60545, 69001, 78209, 88201, 99009, 110665, 123201, 136649, 151041, 166409, 182785, 200201, 218689, 238281, 259009, 280905, 304001
OFFSET
1,1
COMMENTS
a(n) is the difference between numbers of nonnegative multiples of 2*n+1 with even and odd digit sum in base 2*n in interval [0, 32*n^5).
FORMULA
a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^5(Pi*i/(2*n+1)) * sin(2*Pi*i/(2*n+1)).
G.f.: x*(9+29*x-5*x^2-x^3) / (1-x)^4. - Colin Barker, Nov 30 2015
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {9, 65, 201, 449}, 40] (* Vincenzo Librandi, Dec 01 2015 *)
CoefficientList[Series[x (9+29x-5x^2-x^3)/(1-x)^4, {x, 0, 40}], x] (* Harvey P. Dale, Mar 29 2023 *)
PROG
(PARI) a(n)=16*(n+1)*n*(n-1)/3+8*n^2+1 \\ Charles R Greathouse IV, Oct 07 2015
(PARI) Vec(x*(9+29*x-5*x^2-x^3)/(1-x)^4 + O(x^100)) \\ Colin Barker, Nov 30 2015
(Magma) [(16/3)*(n+1)*n*(n-1)+8*n^2+1: n in [1..40]]; // Vincenzo Librandi, Dec 01 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved