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A047397 Numbers that are congruent to {0, 1, 2, 6} mod 8. 1
0, 1, 2, 6, 8, 9, 10, 14, 16, 17, 18, 22, 24, 25, 26, 30, 32, 33, 34, 38, 40, 41, 42, 46, 48, 49, 50, 54, 56, 57, 58, 62, 64, 65, 66, 70, 72, 73, 74, 78, 80, 81, 82, 86, 88, 89, 90, 94, 96, 97, 98, 102, 104, 105, 106, 110, 112, 113, 114, 118, 120, 121, 122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

G.f.: x^2*(1+x+4*x^2+2*x^3) / ( (1+x)*(x^2+1)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011

From Wesley Ivan Hurt, May 24 2016: (Start)

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-11+i^(2*n)+(1+2*i)*i^(-n)+(1-2*i)*i^n)/4, where i=sqrt(-1).

a(2k) = A047452(k), a(2k-1) = A047467(k). (End)

E.g.f.: (4 + 2*sin(x) + cos(x) + (4*x - 6)*sinh(x) + (4*x - 5)*cosh(x))/2. - Ilya Gutkovskiy, May 25 2016

MAPLE

A047397:=n->(8*n-11+I^(2*n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4: seq(A047397(n), n=1..100); # Wesley Ivan Hurt, May 24 2016

MATHEMATICA

Table[(8n-11+I^(2n)+(1+2*I)*I^(-n)+(1-2*I)*I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 24 2016 *)

LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 2, 6, 8}, 70] (* Harvey P. Dale, Dec 31 2017 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 8 in [0, 1, 2, 6]]; // Wesley Ivan Hurt, May 24 2016

CROSSREFS

Cf. A047452, A047467.

Sequence in context: A342751 A120736 A130099 * A174331 A220116 A043341

Adjacent sequences:  A047394 A047395 A047396 * A047398 A047399 A047400

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Wesley Ivan Hurt, May 24 2016

STATUS

approved

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Last modified June 17 22:14 EDT 2021. Contains 345086 sequences. (Running on oeis4.)