A168381 -id:A168381 - cp's OEIS frontend

A168378 a(n) = 3 + 8*floor(n/2).

3, 11, 11, 19, 19, 27, 27, 35, 35, 43, 43, 51, 51, 59, 59, 67, 67, 75, 75, 83, 83, 91, 91, 99, 99, 107, 107, 115, 115, 123, 123, 131, 131, 139, 139, 147, 147, 155, 155, 163, 163, 171, 171, 179, 179, 187, 187, 195, 195, 203, 203, 211, 211, 219, 219, 227, 227, 235, 235

Offset: 1

Vincenzo Librandi, Nov 24 2009

More generally, the sequences generated by the recursive relation b(n) = h*n - b(n-1) + k, with b(1)=c and h, k, c, prefixed integers, have the closed form b(n) = (2*h*n + (3*h + 2*k - 4*c)*(-1)^n + h + 2*k)/4. Also, if 2*c = h+k, then b(n) = c + h*floor(n/2); if 2*c = 2*h+k, then b(n) = c + h*floor((n-1)/2); if 2*c = k, b(n) = c + h*floor((n+1)/2). - Bruno Berselli, Sep 18 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A017101, A168381, A168398.

[3+8*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Table[ 3 + 8*floor(n/2), {n,60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(3 + 8 x - 3 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
LinearRecurrence[{1,1,-1},{3,11,11},80] (* Harvey P. Dale, Oct 05 2022 *)

a(n) = 8*n - a(n-1) - 2, with n>1, a(1)=3.
G.f.: x*(3 + 8*x - 3*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 18 2013
a(n) = 4*n + 2*(-1)^n + 1. - Bruno Berselli, Sep 18 2013
a(n) = A168381(n) + 1 = A168398(n) - 1. - Bruno Berselli, Sep 18 2013
E.g.f.: (4*x + 3)*cosh(x) + (4*x - 1)*sinh(x) - 3. - G. C. Greubel, Jul 19 2016

New definition by Vincenzo Librandi, Sep 18 2013

A168390 a(n) = 1 + 8*floor(n/2).

Original entry on oeis.org

1, 9, 9, 17, 17, 25, 25, 33, 33, 41, 41, 49, 49, 57, 57, 65, 65, 73, 73, 81, 81, 89, 89, 97, 97, 105, 105, 113, 113, 121, 121, 129, 129, 137, 137, 145, 145, 153, 153, 161, 161, 169, 169, 177, 177, 185, 185, 193, 193, 201, 201, 209, 209, 217, 217, 225, 225, 233, 233

Offset: 1

Vincenzo Librandi, Nov 24 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A017077, A168378, A168381.

[1+8*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

RecurrenceTable[{a[1]==1,a[n]==8n-a[n-1]-6},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,9,9},60] (* or *) With[{c=Table[8n+1,{n,0,40}]},Rest[Riffle[c,c]]] (* Harvey P. Dale, Jul 28 2012 *)
Table[1 + 8 Floor[n/2], {n, 60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(1 + 8 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)

a(n) = 8*n - a(n-1) - 6, with n>1, a(1)=1.
a(1)=1, a(2)=9, a(3)=9; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Jul 28 2012
G.f.: x*(1 + 8*x - x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013
a(n) = A168381(n) - 1 = A168378(n) - 2. - Bruno Berselli, Sep 18 2013
E.g.f.: (2 - exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016

New definition by Vincenzo Librandi, Sep 18 2013

cp's OEIS Frontend

A168378 a(n) = 3 + 8*floor(n/2).

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