A047554 Numbers that are congruent to {1, 2, 6, 7} mod 8.

1, 2, 6, 7, 9, 10, 14, 15, 17, 18, 22, 23, 25, 26, 30, 31, 33, 34, 38, 39, 41, 42, 46, 47, 49, 50, 54, 55, 57, 58, 62, 63, 65, 66, 70, 71, 73, 74, 78, 79, 81, 82, 86, 87, 89, 90, 94, 95, 97, 98, 102, 103, 105, 106, 110, 111, 113, 114, 118, 119, 121, 122, 126

Offset

1,2

Links

Table of n, a(n) for n=1..63.

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

Formula

From Wesley Ivan Hurt, May 29 2016: (Start)

G.f.: x*(1+x+4*x^2+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) = 2*n+(1+i)*(2*i-2-(1-i)*i^(2*n)-i^(1-n)+i^n)/4 where i=sqrt(-1).

a(2k) = A047524(k), a(2k-1) = A047452(k). (End)

E.g.f.: (2 - sin(x) + cos(x) + (4*x - 1)*sinh(x) + (4*x - 3)*cosh(x))/2. - Ilya Gutkovskiy, May 30 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/8 (A193887). - Amiram Eldar, Dec 24 2021

Maple

A047554:=n->2*n+(1+I)*(2*I-2-(1-I)*I^(2*n)-I^(1-n)+I^n)/4: seq(A047554(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Select[Range[120], MemberQ[{1, 2, 6, 7}, Mod[#, 8]]&] (* Harvey P. Dale, Nov 29 2011 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 6, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A047452, A047524, A193887.

Sequence in context: A019913 A299421 A327181 * A206446 A079335 A278999

Adjacent sequences: A047551 A047552 A047553 * A047555 A047556 A047557

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved