A253012 a(n) = ceiling( (n+1) * (n+2) / 12).
1, 1, 1, 2, 3, 4, 5, 6, 8, 10, 11, 13, 16, 18, 20, 23, 26, 29, 32, 35, 39, 43, 46, 50, 55, 59, 63, 68, 73, 78, 83, 88, 94, 100, 105, 111, 118, 124, 130, 137, 144, 151, 158, 165, 173, 181, 188, 196, 205, 213, 221, 230, 239, 248, 257, 266, 276, 286, 295, 305
Offset: 0
Examples
G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 4*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 10*x^9 + ...
Links
- G. C. Greubel, Table of n, a(n) for n = 0..2500
- Index entries for linear recurrences with constant coefficients, signature (2,-2,3,-3,2,-2,1).
Programs
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Magma
[Ceiling((n+1)*(n+2)/12): n in [0..60]]; // G. C. Greubel, Aug 04 2018
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Mathematica
a[ n_] := Ceiling[ (n+1) (n+2) / 12];
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PARI
{a(n) = ceil( (n+1) * (n+2) / 12)};
Formula
Euler transform of length 10 sequence [ 1, 0, 1, 1, 1, 0, 0, 0, 0, -1].
G.f.: (1 + x^5) / ((1 - x) * (1 - x^3) * (1 - x^4)) = (1-x+x^2-x^3+x^4) /( (1+x+x^2) *(1+x^2) *(1-x)^3 ).
a(n) = a(-3-n) for all n in Z.
a(n) = A000933(n+5) for all n>=-2.
a(n) - a(n-1) = A091972(n) for all n in Z.
a(n) - 2*a(n+1) + a(n+2) is a period 12 integer sequence.
a(n) - 2*a(n+1) + 2*a(n+2) - 2*a(n+3) + a(n+4) = 1 if n == 1 (mod 3) else 0.