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A317322 Multiples of 22 and odd numbers interleaved.

%I A317322 #33 Dec 11 2024 06:10:03
%S A317322 0,1,22,3,44,5,66,7,88,9,110,11,132,13,154,15,176,17,198,19,220,21,
%T A317322 242,23,264,25,286,27,308,29,330,31,352,33,374,35,396,37,418,39,440,
%U A317322 41,462,43,484,45,506,47,528,49,550,51,572,53,594,55,616,57,638,59,660,61,682,63,704,65,726,67,748,69
%N A317322 Multiples of 22 and odd numbers interleaved.
%C A317322 Partial sums give the generalized 26-gonal numbers (A316724).
%C A317322 a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 26-gonal numbers.
%H A317322 Colin Barker, <a href="/A317322/b317322.txt">Table of n, a(n) for n = 0..1000</a>
%H A317322 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A317322 a(2n) = 22*n, a(2n+1) = 2*n + 1.
%F A317322 From _Colin Barker_, Jul 29 2018: (Start)
%F A317322 G.f.: x*(1 + 22*x + x^2) / ((1 - x)^2*(1 + x)^2).
%F A317322 a(n) = 2*a(n-2) - a(n-4) for n>3. (End)
%F A317322 Multiplicative with a(2^e) = 11*2^e, and a(p^e) = p^e for an odd prime p. - _Amiram Eldar_, Oct 14 2023
%F A317322 Dirichlet g.f.: zeta(s-1) * (1 + 5*2^(2-s)). - _Amiram Eldar_, Oct 26 2023
%t A317322 Module[{nn=40},Riffle[22Range[0,nn],Range[1,2nn,2]]] (* or *) LinearRecurrence[ {0,2,0,-1},{0,1,22,3},80] (* _Harvey P. Dale_, Dec 12 2021 *)
%o A317322 (PARI) concat(0, Vec(x*(1 + 22*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ _Colin Barker_, Jul 29 2018
%Y A317322 Cf. A008604 and A005408 interleaved.
%Y A317322 Column 22 of A195151.
%Y A317322 Sequences whose partial sums give the generalized k-gonal numbers: A026741 (k=5), A001477 (k=6), zero together with A080512 (k=7), A022998 (k=8), A195140 (k=9), zero together with A165998 (k=10), A195159 (k=11), A195161 (k=12), A195312 (k=13), A195817 (k=14).
%Y A317322 Cf. A316724.
%K A317322 nonn,easy,mult
%O A317322 0,3
%A A317322 _Omar E. Pol_, Jul 25 2018