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A047328 Numbers that are congruent to {0, 3, 5, 6} mod 7. 3
0, 3, 5, 6, 7, 10, 12, 13, 14, 17, 19, 20, 21, 24, 26, 27, 28, 31, 33, 34, 35, 38, 40, 41, 42, 45, 47, 48, 49, 52, 54, 55, 56, 59, 61, 62, 63, 66, 68, 69, 70, 73, 75, 76, 77, 80, 82, 83, 84, 87, 89, 90, 91, 94, 96, 97, 98, 101, 103, 104, 105, 108, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Indices of the odd numbers in the Padovan sequence (A000931). - Francesco Daddi, Jul 31 2011

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x^2*(3+2x+x^2+x^3)/((1-x)^2*(1+x)*(1+x^2)). a(n) = A028762(n-2), 2<n<28. - R. J. Mathar, Oct 18 2008

a(n) = (1/8)*(14*n-5-(2-(-1)^n)*(1+2*(-1)^floor(n/2))). - Bruno Berselli, Aug 01 2011

From Wesley Ivan Hurt, May 31 2016: (Start)

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

a(n) = (14*n-7+i^(2*n)-(1+3*i)*i^(-n)-(1-3*i)*i^n)/8 where i=sqrt(-1).

a(2k) = A047280(k), a(2k-1) = A047382(k). (End)

E.g.f.: (4 - 3*sin(x) - cos(x) + (7*x - 4)*sinh(x) + (7*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016

MAPLE

A047328:=n->(14*n-7+I^(2*n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8: seq(A047328(n), n=1..100); # Wesley Ivan Hurt, May 31 2016

MATHEMATICA

Table[(14n-7+I^(2n)-(1+3*I)*I^(-n)-(1-3*I)*I^n)/8, {n, 80}] (* Wesley Ivan Hurt, May 31 2016 *)

PROG

(PARI) a(n)=n\4*7+[0, 3, 5, 6][n%4+1] \\ Charles R Greathouse IV, Jul 31 2011

(MAGMA) [ n: n in [0..111] | n mod 7 in [0, 3, 5, 6] ]; // Bruno Berselli, Aug 01 2011

CROSSREFS

Cf. A000931, A047280, A047382, A134719.

Sequence in context: A067350 A176651 A028762 * A028811 A034035 A335911

Adjacent sequences:  A047325 A047326 A047327 * A047329 A047330 A047331

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 26 08:00 EDT 2021. Contains 348267 sequences. (Running on oeis4.)