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A195159 Multiples of 7 and odd numbers interleaved. 23

%I

%S 0,1,7,3,14,5,21,7,28,9,35,11,42,13,49,15,56,17,63,19,70,21,77,23,84,

%T 25,91,27,98,29,105,31,112,33,119,35,126,37,133,39,140,41,147,43,154,

%U 45,161,47,168,49,175,51,182,53,189,55,196,57,203,59,210,61

%N Multiples of 7 and odd numbers interleaved.

%C This is 7*n if n is even, n if n is odd, if n>=0.

%C Partial sums give the generalized 11-gonal (or hendecagonal) numbers A195160.

%C a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 11-gonal numbers. - _Omar E. Pol_, Jul 27 2018

%C Conjecture: satisfies a linear recurrence having signature (0, 2, 0, -1). - _Harvey P. Dale_, Aug 01 2019

%H Vincenzo Librandi, <a href="/A195159/b195159.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).

%F a(2n) = 7n, a(2n+1) = 2n+1. [corrected by _Omar E. Pol_, Jul 26 2018]

%F From _Bruno Berselli_, Sep 14 2011: (Start)

%F G.f.: x*(1+7*x+x^2)/((1-x)^2*(1+x)^2).

%F a(n) = (5*(-1)^n+9)*n/4.

%F a(n) + a(n-1) = A056020(n). (End)

%F Multiplicative with a(2^e) = 7*2^(e-1), a(p^e) = p^e for odd prime p. - _Andrew Howroyd_, Jul 23 2018

%t Table[If[EvenQ[n], 7(n/2), n], {n, 0, 61}] (* _Alonso del Arte_, Sep 14 2011 *)

%t With[{nn=40},Riffle[7*Range[0,nn],Range[1,2nn,2]]] (* _Harvey P. Dale_, Aug 01 2019 *)

%o (MAGMA) &cat[[7*n, 2*n+1]: n in [0..40]]; // _Vincenzo Librandi_, Sep 27 2011

%o (PARI) a(n)=(5*(-1)^n+9)*n/4 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A008589 and A005408 interleaved.

%Y Column k=7 of A195151.

%Y Cf. Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, this sequence, A195161.

%K nonn,easy,mult

%O 0,3

%A _Omar E. Pol_, Sep 10 2011

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Last modified October 15 07:51 EDT 2019. Contains 328026 sequences. (Running on oeis4.)