A196787 -id:A196787 - cp's OEIS frontend

A196875 a(n) = a(n-4) + a(n-3) + a(n-2) + a(n-1) + (n-5).

1, 1, 1, 1, 4, 8, 16, 32, 64, 125, 243, 471, 911, 1759, 3394, 6546, 12622, 24334, 46910, 90427, 174309, 335997, 647661, 1248413, 2406400, 4638492, 8940988, 17234316, 33220220, 64034041, 123429591, 237918195, 458602075, 883983931, 1703933822, 3284438054

Offset: 1

Aditya Subramanian, Oct 07 2011

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,0,0,-1,1).

Cf. A000126, A196787.

a:= n-> (Matrix(6, (i, j)-> `if`(i=j-1, 1, `if`(i=6, [1, -1, 0, 0, -2, 3][j], 0)))^n. <<-1, 1, 1, 1, 1, 4>>)[1, 1]: seq(a(n), n=1..50); # Alois P. Heinz, Oct 15 2011

nn = 40; a[1] = a[2] = a[3] = a[4] = 1; Do[a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4] + (n - 5), {n, 5, nn}]; Table[a[n], {n, nn}] (* T. D. Noe, Oct 07 2011 *)
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==1,a[n]==a[n-1]+a[n-2]+a[n-3]+a[n-4]+(n-5)},a,{n,40}] (* or *) LinearRecurrence[{3,-2,0,0,-1,1},{1,1,1,1,4,8},40] (* Harvey P. Dale, Aug 25 2014 *)

G.f.: (x^5-3*x^4+2*x-1)*x / ((x^4+x^3+x^2+x-1)*(x-1)^2 ).
a(n) = +3*a(n-1) -2*a(n-2) -a(n-5) +a(n-6).
a(n) = 5/9-n/3 +(10*A000078(n) +17*A000078(n+1) +21*A000078(n+2) -14*A000078(n+3))/9. - R. J. Mathar, Oct 16 2011

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.

Original entry on oeis.org

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

Aditya Subramanian, Oct 07 2011

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.

			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).

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).

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

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 *)

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

cp's OEIS Frontend

A196875 a(n) = a(n-4) + a(n-3) + a(n-2) + a(n-1) + (n-5).

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Formula