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A047541 Numbers that are congruent to {1, 2, 4, 7} mod 8. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 26 13:27 EST 2022. Contains 358362 sequences. (Running on oeis4.)