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%I #20 Sep 08 2022 08:46:10
%S 1,1,2,3,4,6,7,9,11,13,16,18,21,24,27,31,34,38,42,46,51,55,60,65,70,
%T 76,81,87,93,99,106,112,119,126,133,141,148,156,164,172,181,189,198,
%U 207,216,226,235,245,255,265,276,286,297,308,319,331,342,354,366
%N a(n) = floor( n * (n+5) / 10) + 1.
%C If the s(n) are the Somos-4 polynomials, then s(n) = x^a(n-6) * y^a(n-4) * z^a(n-5) * f(n) where f(n) is an irreducible polynomial. - _Michael Somos_, Feb 21 2020
%H G. C. Greubel, <a href="/A249020/b249020.txt">Table of n, a(n) for n = 0..2500</a>
%H Peter H. van der Kamp, <a href="http://arxiv.org/abs/1505.00194">Somos-4 and Somos-5 are arithmetic divisibility sequences</a>, arXiv:1505.00194 [math.NT], 2015.
%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/~somos/somospol.html">Somos Polynomials</a>.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,1,-2,1).
%F G.f.: (1 - x + x^2) / ((1 - x)^2 * (1 - x^5)) = (1-x+x^2)/ ( (1-x)^3*(1+x+x^2+x^3+x^4)).
%F Euler transform of length 6 sequence [1, 1, 1, 0, 1, -1].
%F a(n) = a(-5-n) for all n in Z.
%F a(n) = a(n-5) + n for all n in Z.
%F a(n) + a(n+4) = min( a(n+1) + a(n+3), a(n+2) + a(n+2)) + 1 for all n in Z.
%F a(n) = A249013(n+1) + 1 for all n in Z.
%F a(n) = A008669(n) - A008669(n-6) for all n in Z.
%e G.f. = 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 7*x^6 + 9*x^7 + ...
%e Somos-4 polynomial s(7) = x^1 * y^3 * z^2 * (z + 2*y*z + x*y^2 + y^2*z + x*y*z + x*y^2*z) where 1 = a(7-6), 3 = a(7-4), 2 = a(7-5). - _Michael Somos_, Feb 21 2020
%t a[ n_] := Quotient[ n (n + 5), 10] + 1;
%t CoefficientList[Series[(1-x+x^2)/((1-x)^2*(1-x^5)), {x,0,60}], x] (* or *) Table[Floor[n*(n+5)/10]+1, {n,0,60}] (* _G. C. Greubel_, Aug 04 2018 *)
%o (PARI) {a(n) = n * (n + 5) \ 10 + 1};
%o (PARI) {a(n) = if( n<0, n = -5-n); polcoeff( (1 - x + x^2) / ((1 - x)^2 * (1 - x^5)) + x * O(x^n), n)};
%o (Magma) [Floor(n*(n+5)/10) + 1: n in [0..60]]; // _G. C. Greubel_, Aug 04 2018
%Y Cf. A008669, A249013.
%K nonn,easy
%O 0,3
%A _Michael Somos_, Oct 19 2014
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