A047541 - OEIS

A047541

Numbers that are congruent to {1, 2, 4, 7} mod 8.

1, 2, 4, 7, 9, 10, 12, 15, 17, 18, 20, 23, 25, 26, 28, 31, 33, 34, 36, 39, 41, 42, 44, 47, 49, 50, 52, 55, 57, 58, 60, 63, 65, 66, 68, 71, 73, 74, 76, 79, 81, 82, 84, 87, 89, 90, 92, 95, 97, 98, 100, 103, 105, 106, 108, 111, 113, 114, 116, 119, 121, 122, 124

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OFFSET

1,2

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

FORMULA

From Wesley Ivan Hurt, Jun 04 2016: (Start)

G.f.: x*(1+2*x^2+x^3)/(x-1)^2*(1+x^2).

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4.

a(n) = (1+i)*(n*(4-4*i)+3*i-3+i^(-n)-i^(1+n))/4 where i=sqrt(-1).

a(2k) = A047524(k), a(2k-1) = A047461(k). (End)

E.g.f.: (2 + sin(x) + cos(x) + (4*x - 3)*exp(x))/2. - Ilya Gutkovskiy, Jun 04 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)+1)*Pi/16 - log(2)/8. - Amiram Eldar, Dec 24 2021

MAPLE

A047541:=n->(1+I)*(n*(4-4*I)+3*I-3+I^(-n)-I^(1+n))/4: seq(A047541(n), n=1..100); # Wesley Ivan Hurt, Jun 04 2016

MATHEMATICA

Table[(1+I)*(n*(4-4*I)+3*I-3+I^(-n)-I^(1+n))/4, {n, 80}] (* Wesley Ivan Hurt, Jun 04 2016 *)

Select[Range[200], MemberQ[{1, 2, 4, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[ {2, -2, 2, -1}, {1, 2, 4, 7}, 70] (* Harvey P. Dale, Jul 09 2020 *)

PROG

(PARI) a(n)=n\4*8+[-1, 1, 2, 4][n%4+1] \\ Charles R Greathouse IV, Nov 04 2011

(Magma) [n : n in [0..150] | n mod 8 in [1, 2, 4, 7]]; // Wesley Ivan Hurt, Jun 04 2016

CROSSREFS

Cf. A047461, A047524.

Sequence in context: A327217 A327207 A279934 * A308496 A226812 A185978

Adjacent sequences: A047538 A047539 A047540 * A047542 A047543 A047544

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved