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A133632 a(1)=1, a(n)=(p-1)*a(n-1), if n is even, else a(n)=p*a(n-2), where p=5. 7
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 (list; graph; refs; listen; history; text; internal format)
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

For the partial sums see A133629.

Sequences with similar recurrence rules: A016116(p=2), A038754(p=3), A084221(p=4).

Partial sums for other p: A027383(p=2), A087503(p=3), A133628(p=4).

Other related sequences: A132666, A132667, A132668, A132669.

Cf. A134418, A048875.

Sequence in context: A125995 A080610 A047175 * A163141 A182584 A240860

Adjacent sequences:  A133629 A133630 A133631 * A133633 A133634 A133635

KEYWORD

nonn

AUTHOR

Hieronymus Fischer, Sep 19 2007

STATUS

approved

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Last modified December 7 20:25 EST 2019. Contains 329848 sequences. (Running on oeis4.)