A249013 a(n) = floor( (n-1) * (n+4) / 10 ).

0, 0, 1, 2, 3, 5, 6, 8, 10, 12, 15, 17, 20, 23, 26, 30, 33, 37, 41, 45, 50, 54, 59, 64, 69, 75, 80, 86, 92, 98, 105, 111, 118, 125, 132, 140, 147, 155, 163, 171, 180, 188, 197, 206, 215, 225, 234, 244, 254, 264, 275, 285, 296, 307, 318, 330, 341, 353, 365

Offset: 1

Author

Michael Somos, Oct 19 2014

Keywords

• nonn
• easy

Comments

A028557(n) without the least significant digit. - R. J. Mathar, Aug 11 2021

Examples

			G.f. = x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + 8*x^8 + 10*x^9 + 12*x^10 + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..2500
• Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1,-2,1).

Crossrefs

Cf. A249020, A028557.

Programs

Magma

[Floor((n-1)*(n+4)/10): n in [1..60]]; // Vincenzo Librandi, Jan 10 2015

Mathematica

a[ n_] := Quotient[ (n - 1) (n + 4), 10];
LinearRecurrence[{2, -1, 0, 0, 1, -2, 1}, {0, 0, 1, 2, 3, 5, 6}, 60] (* or *) CoefficientList[Series[x^2 (1 + x^3 - x^4) / ((1 - x)^2 (1 - x^5)), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 10 2015 *)

PARI

{a(n) = (n-1) * (n+4) \ 10};

PARI

{a(n) = if( n<-1, n = -3-n); -(n<1) + polcoeff( x^3*(1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) + x * O(x^n), n)};

Formula

G.f.: x^3 * (1 + x^3 - x^4) / ((1 - x)^2 * (1 - x^5)) = x^3*(1+x^3-x^4)/ ( (1-x)^3*(1+x+x^2+x^3+x^4)).

a(n) = a(-3-n) for all n in Z.

a(n) = a(n-5) + n-1 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.

A249020(n) = a(n+1) + 1 for all n in Z. - Michael Somos, Jan 09 2015