A196876 a(n) = a(n-no-1)+....+a(n-1)+(n-no-2) where no is the 'no+1'th order of the series and 'n' is the element number, here no=6.

1, 1, 1, 1, 1, 1, 1, 7, 14, 28, 56, 112, 224, 448, 896, 1786, 3559, 7091, 14127, 28143, 56063, 111679, 222463, 443141, 882724, 1758358, 3502590, 6977038, 13898014, 27684350, 55146238, 109849336, 218815949, 435873541, 868244493, 1729511949, 3445125885

Offset

1,8

Comments

A196787, A000126, and A000124 are all specific series of this general formula of series. When no=2 the series is A196787. When no=0 the series is A000124 with an additional '1' at the beginning. When no=1 the series is A000126 with an additional '1' at the beginning.

The data given above is the series with no=6 and n=25, having a(1)=.....a(no+1)=1 initially.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,0,0,0,-1,1).

Formula

a(n)=1 if n<=7, else a(n) = n-no-2+sum_{i=1..no+1} a(n-i), no=6.

G.f.: x*( -1+2*x-6*x^7+4*x^8 ) / ( (x^7+x^6+x^5+x^4+x^3+x^2+x-1)*(x-1)^2 ). - R. J. Mathar, Oct 21 2011

Example

For n=25, no=6, then a(1)=1, a(2)=1, ......, a(no)=1 and a(7)=a(1)+a(2)+....a(no)+(6-no), a(8)=a(2)+...a(no+1)+(7-no), a(n)=a(n-no)+....a(n-1)+((n-1)-no) and so a(25)=a(19)+....a(24)+(24-6).

Maple

A196876 := proc(n)
        option remember;
        if n <= 7 then
                1;
        else
                n-6-2+add(procname(n-i), i=1..7) ;
        end if;
end proc: # R. J. Mathar, Oct 21 2011

Mathematica

CoefficientList[Series[(- 1 + 2 x - 6 x^7 + 4 x^8)/((x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1) (x - 1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 11 2012 *)

Crossrefs

Sequence in context: A071711 A290398 A033895 * A115876 A005009 A135092

Adjacent sequences: A196873 A196874 A196875 * A196877 A196878 A196879

Keyword

nonn,easy

Author

Aditya Subramanian, Oct 07 2011

Status

approved