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A047427 Numbers that are congruent to {1, 3, 4, 5, 6} mod 8. 1
1, 3, 4, 5, 6, 9, 11, 12, 13, 14, 17, 19, 20, 21, 22, 25, 27, 28, 29, 30, 33, 35, 36, 37, 38, 41, 43, 44, 45, 46, 49, 51, 52, 53, 54, 57, 59, 60, 61, 62, 65, 67, 68, 69, 70, 73, 75, 76, 77, 78, 81, 83, 84, 85, 86, 89, 91, 92, 93, 94, 97, 99, 100, 101, 102 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..65.

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

FORMULA

G.f.: x*(1+2*x+x^2+x^3+x^4+2*x^5) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Aug 01 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6, a(n) = a(n-5) + 8 for n > 5.

a(n) = (40*n - 25 + 3*(n mod 5) + 3*((n+1) mod 5) + 3*((n+2) mod 5) - 2*((n+3) mod 5) - 7*((n+4) mod 5))/25.

a(5k) = 8k-2, a(5k-1) = 8k-3, a(5k-2) = 8k-4, a(5k-3) = 8k-5, a(5k-4) = 8k-7. (End)

MAPLE

A047427:=n->8*floor(n/5)+[(1, 3, 4, 5, 6)][(n mod 5)+1]: seq(A047427(n), n=0..100); # Wesley Ivan Hurt, Aug 01 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{1, 3, 4, 5, 6}, Mod[#, 8]] &] (* Wesley Ivan Hurt, Aug 01 2016 *)

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {1, 3, 4, 5, 6, 9}, 70] (* Harvey P. Dale, Dec 15 2018 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [1, 3, 4, 5, 6]]; // Wesley Ivan Hurt, Aug 01 2016

(PARI) a(n)=[-2, 1, 3, 4, 5][n%5+1] + n\5*8 \\ Charles R Greathouse IV, Aug 01 2016

CROSSREFS

Sequence in context: A136681 A206330 A104373 * A228235 A228895 A267322

Adjacent sequences:  A047424 A047425 A047426 * A047428 A047429 A047430

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 26 20:33 EST 2020. Contains 331288 sequences. (Running on oeis4.)