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A047442 Numbers that are congruent to {0, 1, 2, 5, 6} mod 8. 1

%I #16 Sep 08 2022 08:44:57

%S 0,1,2,5,6,8,9,10,13,14,16,17,18,21,22,24,25,26,29,30,32,33,34,37,38,

%T 40,41,42,45,46,48,49,50,53,54,56,57,58,61,62,64,65,66,69,70,72,73,74,

%U 77,78,80,81,82,85,86,88,89,90,93,94,96,97,98,101,102,104

%N Numbers that are congruent to {0, 1, 2, 5, 6} mod 8.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,1,-1).

%F G.f.: x^2*(x^2+1)*(2*x^2+x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - _R. J. Mathar_, Dec 07 2011

%F From _Wesley Ivan Hurt_, Aug 01 2016: (Start)

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

%F a(n) = (40*n - 50 + 3*(n mod 5) - 7*((n+1) mod 5) + 3*((n+2) mod 5) + 3*((n+3) mod 5) - 2*((n+4) mod 5))/25.

%F a(5k) = 8k-2, a(5k-1) = 8k-3, a(5k-2) = 8k-6, a(5k-3) = 8k-7, a(5k-4) = 8k-8. (End)

%p A047442:=n->8*floor(n/5)+[(0, 1, 2, 5, 6)][(n mod 5)+1]: seq(A047442(n), n=0..100); # _Wesley Ivan Hurt_, Aug 01 2016

%t Select[Range[0, 100], MemberQ[{0, 1, 2, 5, 6}, Mod[#, 8]] &] (* _Wesley Ivan Hurt_, Aug 01 2016 *)

%o (Magma) [n : n in [0..150] | n mod 8 in [0, 1, 2, 5, 6]]; // _Wesley Ivan Hurt_, Aug 01 2016

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)