A133632 - OEIS

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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.

1, 4, 5, 20, 25, 100, 125, 500, 625, 2500, 3125, 12500, 15625, 62500, 78125, 312500, 390625, 1562500, 1953125, 7812500, 9765625, 39062500, 48828125, 195312500, 244140625, 976562500, 1220703125, 4882812500, 6103515625, 24414062500

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OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..30.

Index entries for linear recurrences with constant coefficients, signature (0, 5).

FORMULA

The following formulas are given for a general natural parameter p > 1 (p = 5 for this sequence).

G.f.: g(x) = x(1+(p-1)x)/(1-px^2).

a(n) = p^floor((n-1)/2)*(p+(p-2)*(-1)^n)/2.

a(n) = A133629(n) - A133629(n-1) for n > 1.

a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011

MATHEMATICA

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 *)

CROSSREFS