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

Offset: 1

Author

Vladimir Shevelev and Peter J. C. Moses, May 23 2012

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A038754, A084990, A091042, A212500, A212592, A212592, A212592, A212668.

Programs

PARI

Vec(2*x*(9+116*x+126*x^2+4*x^3+x^4)/(1-x)^6 + O(x^50)) \\ Colin Barker, Dec 01 2015

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