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A212670 a(n) = 1/15*(128*n^5 + 320*n^4 + 80*n^3 - 200*n^2 + 92*n - 15). 4
27, 615, 3843, 14351, 40363, 94711, 195859, 368927, 646715, 1070727, 1692195, 2573103, 3787211, 5421079, 7575091, 10364479, 13920347, 18390695, 23941443, 30757455, 39043563, 49025591, 60951379, 75091807, 91741819, 111221447, 133876835, 160081263, 190236171 (list; graph; refs; listen; history; text; internal format)
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, 128*n^7).
LINKS
FORMULA
a(n) = 2/(2*n+1)*Sum_{i=1..n} tan^7(Pi*i/(2*n+1))*sin(2*Pi*i/(2*n+1)).
G.f.: x*(27+453*x+558*x^2-22*x^3+7*x^4+x^5)/(1-x)^6. [Bruno Berselli, May 24 2012]
MATHEMATICA
Table[(1/15) (8 n^2 - 4 n + 1) (16 n^3 + 48 n^2 + 32 n - 15), {n, 29}] (* Bruno Berselli, May 24 2012 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {27, 615, 3843, 14351, 40363, 94711}, 30] (* Harvey P. Dale, Apr 30 2018 *)
PROG
(PARI) Vec(x*(27+453*x+558*x^2-22*x^3+7*x^4+x^5)/(1-x)^6 + O(x^50)) \\ Colin Barker, Dec 01 2015
CROSSREFS
Sequence in context: A232944 A185891 A185883 * A099753 A231292 A046359
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved

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Last modified April 18 02:55 EDT 2024. Contains 371767 sequences. (Running on oeis4.)