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a(4*n)=5^n, a(4*n+1)=2*5^n, a(4*n+2)=3*5^n, a(4*n+3)=4*5^n.
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%I #24 Jan 19 2023 02:17:26

%S 1,2,3,4,5,10,15,20,25,50,75,100,125,250,375,500,625,1250,1875,2500,

%T 3125,6250,9375,12500,15625,31250,46875,62500,78125,156250,234375,

%U 312500,390625,781250,1171875,1562500,1953125,3906250,5859375,7812500

%N a(4*n)=5^n, a(4*n+1)=2*5^n, a(4*n+2)=3*5^n, a(4*n+3)=4*5^n.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,5).

%F a(n+1) = a(n) + a(n - n mod 4).

%F a(n) = A140740(n+4,4).

%F O.g.f.: (1+2*x+3*x^2+4*x^3)/(1-5*x^4). - _R. J. Mathar_, May 31 2008

%F a(n) = (n+1-4*floor(n/4))*5^floor(n/4). - _Luce ETIENNE_, Aug 05 2015

%F a(n) = 5*a(n-4) for n>3; a(n) = n+1 for n<5. - _Bruno Berselli_, Aug 05 2015

%F Sum_{n>=0} 1/a(n) = 125/48. - _Amiram Eldar_, Jan 21 2022

%t Table[(n + 1 - 4 Floor[n/4]) 5^Floor[n/4], {n, 0, 40}] (* _Bruno Berselli_, Aug 05 2015 *)

%t LinearRecurrence[{0,0,0,5},{1,2,3,4},40] (* _Harvey P. Dale_, Jul 01 2022 *)

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

%o (Python)

%o def A140730(n): return ((n&3)+1)*5**(n>>2) # _Chai Wah Wu_, Jan 18 2023

%Y Cf. A000079, A037124, A038754, A133464, A140740.

%K nonn,easy

%O 0,2

%A _Reinhard Zumkeller_, May 26 2008