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

Offset: 1

Author

Hieronymus Fischer, Sep 19 2007

Keywords

• nonn

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

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

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.

Programs

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 *)

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