A100531 a(n) = a(n-1) + (2*n - 1) mod 8 + 1 with a(0)=1.

1, 3, 7, 13, 21, 23, 27, 33, 41, 43, 47, 53, 61, 63, 67, 73, 81, 83, 87, 93, 101, 103, 107, 113, 121, 123, 127, 133, 141, 143, 147, 153, 161, 163, 167, 173, 181, 183, 187, 193, 201, 203, 207, 213, 221, 223, 227, 233, 241, 243, 247, 253, 261, 263, 267, 273, 281, 283

Offset

0,2

Comments

Numbers == 1, 3, 7, 13 modulo 20. - Ralf Stephan, May 15 2007

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = a(n-1) + a(n-4) - a(n-5), with a(0)=1, a(1)=3, a(2)=7, a(3)=13, a(4)=21. - Harvey P. Dale, Apr 09 2012

G.f.: (1+2*x+4*x^2+6*x^3+7*x^4)/((1-x)^2*(1+x+x^2+x^3)). - Harvey P. Dale, Apr 09 2012

a(n) = 5*n - (3-(-1)^n)/2 + i^n + (-i)^n, where i=sqrt(-1). - Colin Barker, Oct 16 2015

E.g.f.: (5*x-1)*cosh(x) + (5*x-2)*sinh(x) + 2*cos(x). - G. C. Greubel, Jun 30 2022

Mathematica

f[n_]:= f[n]= If[n==0, 1, f[n-1]+Mod[2*n-1, 8]+1]; Table[f[n], {n, 0, 100}]
RecurrenceTable[{a[0]==1, a[n]==a[n-1]+Mod[2n-1, 8]+1}, a, {n, 60}] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 3, 7, 13, 21}, 60] (* Harvey P. Dale, Apr 09 2012 *)

Prog

(PARI) a(n) = (5*n-3/2+(-1)^n/2+(-I)^n+I^n) \\ Colin Barker, Oct 16 2015
(PARI) Vec((7*x^4+6*x^3+4*x^2+2*x+1)/((x-1)^2*(x^3+x^2+x+1)) + O(x^100)) \\ Colin Barker, Oct 16 2015
(Magma) [n mod 2 eq 0 select Round(5*n-1+2*(-1)^(n/2)) else Round(5*n-2): n in [0..100]]; // G. C. Greubel, Jun 30 2022
(SageMath) [5*n-1 -(n%2) +2*i^n*((n+1)%2) for n in (0..60)] # G. C. Greubel, Jun 30 2022

Crossrefs

Sequence in context: A076950 A169633 A069194 * A032409 A073896 A299478

Adjacent sequences: A100528 A100529 A100530 * A100532 A100533 A100534

Keyword

nonn,easy

Author

Roger L. Bagula, Nov 24 2004

Status

approved