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

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.

Sequence in context: A102046 A019913 A299421 * A206446 A079335 A278999

Adjacent sequences:  A047551 A047552 A047553 * A047555 A047556 A047557

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 26 22:57 EDT 2019. Contains 323597 sequences. (Running on oeis4.)