A036409 a(n) = ceiling(n^2/11).
0, 1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 11, 14, 16, 18, 21, 24, 27, 30, 33, 37, 41, 44, 49, 53, 57, 62, 67, 72, 77, 82, 88, 94, 99, 106, 112, 118, 125, 132, 139, 146, 153, 161, 169, 176, 185, 193, 201, 210, 219, 228, 237, 246, 256, 266, 275, 286, 296
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,1,-2,1).
Programs
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Maple
seq(ceil(n^2/11),n=0..100); # Robert Israel, Apr 06 2016
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Mathematica
Table[Ceiling[n^2/11], {n, 0, 57}] (* Michael De Vlieger, Apr 06 2016 *) LinearRecurrence[{2,-1,0,0,0,0,0,0,0,0,1,-2,1},{0,1,1,1,2,3,4,5,6,8,10,11,14},60] (* Harvey P. Dale, Aug 29 2021 *) -
PARI
concat(0, Vec(x*(1+x)*(1-x+x^2)*(1-x+x^2-x^3+x^4)*(1-x^2+x^4) / ((1-x)^3*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)) + O(x^50))) \\ Colin Barker, Apr 06 2016
Formula
a(n) = +2 a(n-1) -a(n-2) +a(n-11) -2 a(n-12) +a(n-13). - R. J. Mathar, Mar 11 2012
G.f.: x*(1+x)*(1-x+x^2)*(1-x+x^2-x^3+x^4)*(1-x^2+x^4) / ((1-x)^3*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10)). - Colin Barker, Apr 06 2016
a(m + 11 k) = a(m) + 11 k^2 + 2 m k. - Robert Israel, Apr 06 2016