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A255413 a(n) = 15*n - 11 + (n mod 2). Row 3 of Ludic array A255127.

%I A255413 #31 Nov 13 2024 01:54:32
%S A255413 5,19,35,49,65,79,95,109,125,139,155,169,185,199,215,229,245,259,275,
%T A255413 289,305,319,335,349,365,379,395,409,425,439,455,469,485,499,515,529,
%U A255413 545,559,575,589,605,619,635,649,665,679,695,709,725,739,755,769,785,799,815,829,845,859,875,889,905,919,935,949,965,979,995,1009
%N A255413 a(n) = 15*n - 11 + (n mod 2). Row 3 of Ludic array A255127.
%H A255413 Antti Karttunen, <a href="/A255413/b255413.txt">Table of n, a(n) for n = 1..10001</a>
%H A255413 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A255413 a(n) = A007310((5*n)-3).
%F A255413 a(n) = A255407(A084967(n)) = A255407(5*A007310(n)).
%F A255413 a(2n+1) = 5*A016921(n) for all n >= 0.
%F A255413 From _M. F. Hasler_, Nov 09 2024: (Start)
%F A255413 a(n) = a(n-1) + a(n-2) + a(n-3) for n > 3, a(1..3) = (5, 19, 35).
%F A255413 a(n) = a(n-2) + 30 for n > 2, with a(1..2) = (5, 19).
%F A255413 a(2n-1) = 30n - 25, a(2n) = 30n - 11.
%F A255413 G.f.: x*(5 + 14*x + 11*x^2)/((1 - x)^2*(1 + x)). (End)
%F A255413 E.g.f.: 11 + (15*x - 11)*cosh(x) + 5*(3*x - 2)*sinh(x). - _Stefano Spezia_, Nov 12 2024
%t A255413 a[n_] := 15 n + Mod[n, 2] - 11;
%t A255413 Array[a, 100] (* _Jean-François Alcover_, Mar 14 2016 *)
%o A255413 (Scheme) ;; two alternatives:
%o A255413 (define (A255413 n) (A255127bi 3 n)) ;; Code for A255127bi given in A255127.
%o A255413 (define (A255413 n) (A007310 (- (* 5 n) 3)))
%o A255413 (PARI) apply( {A255413(n)=15*n-11+n%2}, [1..50]) \\ _M. F. Hasler_, Nov 09 2024
%Y A255413 Row 3 of A255127.
%Y A255413 Cf. A007310, A016921, A084967, A255407.
%K A255413 nonn,easy
%O A255413 1,1
%A A255413 _Antti Karttunen_, Feb 22 2015
%E A255413 New definition from _M. F. Hasler_, Nov 09 2024