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A047544 Numbers that are congruent to {1, 3, 4, 7} mod 8. 1
1, 3, 4, 7, 9, 11, 12, 15, 17, 19, 20, 23, 25, 27, 28, 31, 33, 35, 36, 39, 41, 43, 44, 47, 49, 51, 52, 55, 57, 59, 60, 63, 65, 67, 68, 71, 73, 75, 76, 79, 81, 83, 84, 87, 89, 91, 92, 95, 97, 99, 100, 103, 105, 107, 108, 111, 113, 115, 116, 119, 121, 123, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
From Wesley Ivan Hurt, May 29 2016: (Start)
G.f.: x*(1+2*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) = (8*n-5+i^(2*n)+i^(1-n)-i^(1+n))/4 where i=sqrt(-1).
a(2k) = A004767(k-1) for n>0, a(2k-1) = A047461(k). (End)
E.g.f.: (2 + sin(x) + (4*x - 3)*sinh(x) + (4*x - 2)*cosh(x))/2. - Ilya Gutkovskiy, May 29 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+3)*Pi/16 - log(2)/4 + sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 24 2021
MAPLE
A047544:=n->(8*n-5+I^(2*n)+I^(1-n)-I^(1+n))/4: seq(A047544(n), n=1..100); # Wesley Ivan Hurt, May 29 2016
MATHEMATICA
Table[(8n-5+I^(2n)+I^(1-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 3, 4, 7, 9}, 50] (* G. C. Greubel, May 29 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 3, 4, 7]]; // Wesley Ivan Hurt, May 29 2016
CROSSREFS
Sequence in context: A019990 A288634 A284776 * A272909 A035267 A309133
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified July 18 06:23 EDT 2024. Contains 374377 sequences. (Running on oeis4.)