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A047507
Numbers that are congruent to {0, 4, 6, 7} mod 8.
2
0, 4, 6, 7, 8, 12, 14, 15, 16, 20, 22, 23, 24, 28, 30, 31, 32, 36, 38, 39, 40, 44, 46, 47, 48, 52, 54, 55, 56, 60, 62, 63, 64, 68, 70, 71, 72, 76, 78, 79, 80, 84, 86, 87, 88, 92, 94, 95, 96, 100, 102, 103, 104, 108, 110, 111, 112, 116, 118, 119, 120, 124
OFFSET
1,2
FORMULA
G.f.: x^2*(4+2*x+x^2+x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Nov 06 2015
From Wesley Ivan Hurt, May 27 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (8*n-3+i^(2*n)-(1+2*i)*i^(-n)-(1-2*i)*i^n)/4 where i=sqrt(-1).
a(2k) = A047535(k), a(2k-1) = A047451(k). (End)
E.g.f.: (2 - 2*sin(x) - cos(x) + (4*x - 2)*sinh(x) + (4*x - 1)*cosh(x))/2. - Ilya Gutkovskiy, May 27 2016
Sum_{n>=2} (-1)^n/a(n) = (6-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 23 2021
a(n) = -A003485(-n) = a(n+4) - 8 for all n in Z. - Michael Somos, Dec 12 2023
EXAMPLE
G.f. = 4*x^2 + 6*x^3 + 7*x^4 + 8*x^5 + 12*x^6 + 14*x^7 + 15*x^8 + 16*x^9 + ... - Michael Somos, Dec 12 2023
MAPLE
A047507:=n->(8*n-3+I^(2*n)-(1+2*I)*I^(-n)-(1-2*I)*I^n)/4: seq(A047507(n), n=1..100); # Wesley Ivan Hurt, May 27 2016
MATHEMATICA
Table[(8n-3+I^(2n)-(1+2*I)*I^(-n)-(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 27 2016 *)
a[ n_] := 2*n - Max[0, 2 - Mod[1-n, 4]]; (* Michael Somos, Dec 12 2023 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [0, 4, 6, 7]]; // Wesley Ivan Hurt, May 27 2016
(PARI) {a(n) = 2*n - max(0, 2 - (1-n)%4)}; /* Michael Somos, Dec 12 2023 */
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved