A174396 Numbers congruent to {1,4,5,8} mod 9.

1, 4, 5, 8, 10, 13, 14, 17, 19, 22, 23, 26, 28, 31, 32, 35, 37, 40, 41, 44, 46, 49, 50, 53, 55, 58, 59, 62, 64, 67, 68, 71, 73, 76, 77, 80, 82, 85, 86, 89, 91, 94, 95, 98, 100, 103, 104, 107, 109, 112, 113, 116, 118, 121, 122, 125, 127, 130, 131, 134, 136

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 3*(n-1-floor((n-1)/4)) + (-1)^floor((n-1)/2).

From Wesley Ivan Hurt, Oct 17 2015: (Start)

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

a(n) = a(n-1)+a(n-4)-a(n-5) for n>5.

a(n) = (18*n-9+3*(-1)^n-2*(-1)^((2*n+1-(-1)^n)/4))/8. (End)

E.g.f.: (1/8)*(2*sin(x) - 2*cos(x) + 18*x*exp(x) + 3*exp(-x) - 9*exp(x) + 8). - G. C. Greubel, Oct 18 2015

Maple

seq(3*(n - floor(n/4)) + (-1)^floor(n/2), n=0..100);

Mathematica

CoefficientList[Series[(1 + 3 x + x^2 + 3 x^3 + x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Oct 17 2015 *)
RecurrenceTable[{a[1] == 1, a[2] == 4, a[3] == 5, a[4] == 8, a[5] == 10 , a[n+5] == a[n+4] + a[n+1] - a[n] }, a, {n, 1, 100}] (* G. C. Greubel, Oct 18 2015 *)

Prog

(Magma) [(18*n-9+3*(-1)^n-2*(-1)^((2*n+1-(-1)^n) div 4))/8 : n in [1..100]]; // Wesley Ivan Hurt, Oct 17 2015

Crossrefs

Sequence in context: A292658 A304108 A214026 * A033157 A310574 A059659

Adjacent sequences: A174393 A174394 A174395 * A174397 A174398 A174399

Keyword

nonn,easy

Author

Gary Detlefs, Mar 18 2010

Extensions

Formula corrected by Gary Detlefs, Mar 19 2010

Status

approved