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Search: id:A133632
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| A133632 |
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a(1)=1, a(n)=(p-1)*a(n-1), if n is even, else a(n)=p*a(n-2), where p=5. |
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8
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| 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
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1,2
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COMMENT
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Binomial transform = A134418: (1, 5, 14, 48, 152, 496, 1600,...). Double binomial transform = A048875: (1, 6, 25, 106, 449, 1902,...) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 24 2007
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FORMULA
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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.
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CROSSREFS
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For the partial sums see A133629.
Sequences with similar recurrence rules: A016116(p=2), A133626(p=3), A084221(p=4).
Partial sums for other p: A027383(p=2), A133627(p=3), A133628(p=4).
Other related sequences: A132666, A132667, A132668, A132669.
Cf. A134418, A048875.
Sequence in context: A125995 A080610 A047175 this_sequence A059182 A027958 A064670
Adjacent sequences: A133629 A133630 A133631 this_sequence A133633 A133634 A133635
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
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