A289199 a(n) is the number of odd integers divisible by 13 in the open interval (12*(n-1)^2, 12*n^2).
0, 0, 2, 2, 3, 5, 5, 6, 7, 7, 9, 10, 10, 12, 12, 14, 14, 15, 17, 17, 18, 19, 19, 21, 22, 22, 24, 24, 26, 26, 27, 29, 29, 30, 31, 31, 33, 34, 34, 36, 36, 38, 38, 39, 41, 41, 42, 43, 43, 45, 46, 46, 48, 48, 50, 50, 51, 53, 53, 54, 55, 55, 57, 58, 58, 60, 60, 62, 62, 63, 65
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,1,-1).
Programs
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Mathematica
Table[Count[Mod[Table[2(6(n-1)^2 +k)-1,{k,12 n-6}],13],0],{n,0,70}] -
PARI
a(n)=(12*n^2+12)\26 - (12*n^2-24*n+25)\26 \\ Charles R Greathouse IV, Jun 29 2017
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PARI
concat(vector(2), Vec(x^2*(1 + x)*(1 - x + x^2)*(2 + x^2 + x^6 + 2*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)) + O(x^100))) \\ Colin Barker, Jul 03 2017
Formula
a(n + 13*k) = a(n) + 12*k.
a(n) = 12n/13 + O(1). - Charles R Greathouse IV, Jun 29 2017
From Colin Barker, Jul 03 2017: (Start)
G.f.: x^2*(1 + x)*(1 - x + x^2)*(2 + x^2 + x^6 + 2*x^8) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12)).
a(n) = a(n-1) + a(n-13) - a(n-14) for n>13.
(End)
Comments