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A133632 a(1)=1, a(n) = (p-1)*a(n-1), if n is even, otherwise a(n) = p*a(n-2), where p = 5.

%I A133632 #17 Feb 08 2022 20:00:35
%S A133632 1,4,5,20,25,100,125,500,625,2500,3125,12500,15625,62500,78125,312500,
%T A133632 390625,1562500,1953125,7812500,9765625,39062500,48828125,195312500,
%U A133632 244140625,976562500,1220703125,4882812500,6103515625,24414062500
%N A133632 a(1)=1, a(n) = (p-1)*a(n-1), if n is even, otherwise a(n) = p*a(n-2), where p = 5.
%C A133632 Binomial transform = A134418: (1, 5, 14, 48, 152, 496, 1600, ...). Double binomial transform = A048875: (1, 6, 25, 106, 449, 1902, ...) - _Gary W. Adamson_, Oct 24 2007
%H A133632 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0, 5).
%F A133632 The following formulas are given for a general natural parameter p > 1 (p = 5 for this sequence).
%F A133632 G.f.: g(x) = x(1+(p-1)x)/(1-px^2).
%F A133632 a(n) = p^floor((n-1)/2)*(p+(p-2)*(-1)^n)/2.
%F A133632 a(n) = A133629(n) - A133629(n-1) for n > 1.
%F A133632 a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%t A133632 RecurrenceTable[{a[1]==1,a[2]==4,a[n]==If[EvenQ[n],4a[n-1],5a[n-2]]},a,{n,30}] (* _Harvey P. Dale_, Jan 14 2013 *)
%Y A133632 For the partial sums see A133629.
%Y A133632 Sequences with similar recurrence rules: A016116(p=2), A038754(p=3), A084221(p=4).
%Y A133632 Partial sums for other p: A027383(p=2), A087503(p=3), A133628(p=4).
%Y A133632 Other related sequences: A132666, A132667, A132668, A132669.
%Y A133632 Cf. A134418, A048875.
%K A133632 nonn
%O A133632 1,2
%A A133632 _Hieronymus Fischer_, Sep 19 2007