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A212669

a(n) = 2/15 * (32*n^5 + 80*n^4 + 40*n^3 - 20*n^2 + 3*n).

18, 340, 2022, 7400, 20602, 48060, 99022, 186064, 325602, 538404, 850102, 1291704, 1900106, 2718604, 3797406, 5194144, 6974386, 9212148, 11990406, 15401608, 19548186, 24543068, 30510190, 37585008, 45915010, 55660228, 66993750, 80102232, 95186410, 112461612

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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, 64*n^6).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

V. Shevelev, On monotonic strengthening of Newman-like phenomenon on (2m+1)-multiples in base 2m, arXiv:0710.3177 [math.NT], 2007.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^6(Pi*i/(2*n+1)).

G.f.: 2*x*(9+116*x+126*x^2+4*x^3+x^4) / (1-x)^6. - Colin Barker, Dec 01 2015