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A047356
Numbers that are congruent to {1, 3} mod 7.
6
1, 3, 8, 10, 15, 17, 22, 24, 29, 31, 36, 38, 43, 45, 50, 52, 57, 59, 64, 66, 71, 73, 78, 80, 85, 87, 92, 94, 99, 101, 106, 108, 113, 115, 120, 122, 127, 129, 134, 136, 141, 143, 148, 150, 155, 157, 162, 164, 169
OFFSET
1,2
COMMENTS
This sequence is related to A010702 by a(n) = (Sum_{i=1..n} A010702(i)) - A010702(n+1). - Bruno Berselli, Mar 12 2012
FORMULA
a(n) = 7*n - a(n-1) - 10 with n > 1, a(1)=1. - Vincenzo Librandi, Aug 05 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 7*n/2 - 13/4 - 3*(-1)^n/4.
G.f.: x*(1+2*x+4*x^2) / ( (1+x)*(x-1)^2 ). (End)
E.g.f.: 4 + ((14*x - 13)*exp(x) - 3*exp(-x))/4. - David Lovler, Sep 11 2022
MATHEMATICA
With[{c=7 Range[0, 50]}, Sort[Join[c+1, c+3]]] (* or *) LinearRecurrence[ {1, 1, -1}, {1, 3, 8}, 100] (* Harvey P. Dale, May 29 2012 *)
PROG
(PARI) a(n) = (14*n - 13 - 3*(-1)^n)/4 \\ David Lovler, Sep 11 2022
CROSSREFS
Cf. A010702.
Sequence in context: A003038 A184870 A073547 * A083246 A023492 A022801
KEYWORD
nonn,easy
STATUS
approved