%I #17 Sep 08 2022 08:46:10
%S 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,
%T 63,68,73,78,83,88,94,100,105,111,118,124,130,137,144,151,158,165,173,
%U 181,188,196,205,213,221,230,239,248,257,266,276,286,295,305
%N a(n) = ceiling( (n+1) * (n+2) / 12).
%H G. C. Greubel, <a href="/A253012/b253012.txt">Table of n, a(n) for n = 0..2500</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,3,-3,2,-2,1).
%F Euler transform of length 10 sequence [ 1, 0, 1, 1, 1, 0, 0, 0, 0, -1].
%F 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 ).
%F a(n) = a(-3-n) for all n in Z.
%F a(n) = A000933(n+5) for all n>=-2.
%F a(n) - a(n-1) = A091972(n) for all n in Z.
%F a(n) - 2*a(n+1) + a(n+2) is a period 12 integer sequence.
%F 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.
%e 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 + ...
%t a[ n_] := Ceiling[ (n+1) (n+2) / 12];
%o (PARI) {a(n) = ceil( (n+1) * (n+2) / 12)};
%o (Magma) [Ceiling((n+1)*(n+2)/12): n in [0..60]]; // _G. C. Greubel_, Aug 04 2018
%Y Cf. A000933, A091972.
%K nonn,easy
%O 0,4
%A _Michael Somos_, Dec 25 2014