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A174396 Numbers congruent to {1,4,5,8} mod 9. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A026491 A255491 A214026 * A033157 A059659 A140459

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

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Last modified August 18 12:32 EDT 2017. Contains 290720 sequences.