A249020 a(n) = floor( n * (n+5) / 10) + 1.

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, 76, 81, 87, 93, 99, 106, 112, 119, 126, 133, 141, 148, 156, 164, 172, 181, 189, 198, 207, 216, 226, 235, 245, 255, 265, 276, 286, 297, 308, 319, 331, 342, 354, 366

Offset: 0

Author

Michael Somos, Oct 19 2014

Keywords

• nonn
• easy

Comments

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

Examples

			G.f. = 1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 6*x^5 + 7*x^6 + 9*x^7 + ...
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
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Peter H. van der Kamp, Somos-4 and Somos-5 are arithmetic divisibility sequences, arXiv:1505.00194 [math.NT], 2015.
• Michael Somos, Somos Polynomials.
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Crossrefs

Cf. A008669, A249013.

Programs

Magma

[Floor(n*(n+5)/10) + 1: n in [0..60]]; // G. C. Greubel, Aug 04 2018

Mathematica

a[ n_] := Quotient[ n (n + 5), 10] + 1;
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 *)

PARI

{a(n) = n * (n + 5) \ 10 + 1};

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)};

Formula

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)).

Euler transform of length 6 sequence [1, 1, 1, 0, 1, -1].

a(n) = a(-5-n) for all n in Z.

a(n) = a(n-5) + n for all n in Z.

a(n) + a(n+4) = min( a(n+1) + a(n+3), a(n+2) + a(n+2)) + 1 for all n in Z.

a(n) = A249013(n+1) + 1 for all n in Z.

a(n) = A008669(n) - A008669(n-6) for all n in Z.