A047540 Numbers that are congruent to {0, 2, 4, 7} mod 8.
0, 2, 4, 7, 8, 10, 12, 15, 16, 18, 20, 23, 24, 26, 28, 31, 32, 34, 36, 39, 40, 42, 44, 47, 48, 50, 52, 55, 56, 58, 60, 63, 64, 66, 68, 71, 72, 74, 76, 79, 80, 82, 84, 87, 88, 90, 92, 95, 96, 98, 100, 103, 104, 106, 108, 111, 112, 114, 116, 119, 120, 122, 124
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Programs
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Magma
[n : n in [0..150] | n mod 8 in [0, 2, 4, 7]]; // Wesley Ivan Hurt, May 29 2016
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Maple
A047540:=n->(8*n-7+I^(2*n)+I^(-n)+I^n)/4: seq(A047540(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
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Mathematica
Table[(8n-7+I^(2n)+I^(-n)+I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *) {0,2,4,7}+#&/@(8*Range[0,20])//Flatten (* Harvey P. Dale, Dec 20 2022 *)
Formula
From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x^2*(2+2*x+3*x^2+x^3) / ((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) = (8*n-7+i^(2*n)+i^(-n)+i^n)/4 where i=sqrt(-1).
Sum_{n>=2} (-1)^n/a(n) = (10-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 21 2021
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