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Search: id:A133629
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| A133629 |
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a(1)=1, a(n)=a(n-1)+(p-1)*p^(n/2-1) if n is even, else a(n)=a(n-1)+p^((n-1)/2), where p=5. |
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7
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| 1, 5, 10, 30, 55, 155, 280, 780, 1405, 3905, 7030, 19530, 35155, 97655, 175780, 488280, 878905, 2441405, 4394530, 12207030, 21972655, 61035155, 109863280, 305175780, 549316405, 1525878905, 2746582030, 7629394530, 13732910155
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OFFSET
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1,2
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COMMENT
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Partial sums of A133632.
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FORMULA
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a(n)=sum{1<=k<=n, A133632(k)}.
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)(1-x)).
a(n)=(p/(p-1))*(p^(n/2)-1) if n is even, else a(n)=(p/(p-1))*((2p-1)*p^((n-3)/2)-1).
a(n)=(p/(p-1))*(p^floor(n/2)+p^floor((n-1)/2)-p^floor((n-2)/2)-1).
a(n)=p^floor(n/2)+(p^floor((n+1)/2)-p)/(p-1).
a(n)=A132669(a(n+1))-1.
a(n)=A132669(a(n-1)+1) for n>0.
A132669(a(n))=a(n-1)+1 for n>0.
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=5*a[n-2]+5 od: seq(a[n], n=1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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CROSSREFS
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Sequences with similar recurrence rules: A027383(p=2), A133627(p=3), A133629(p=5).
Related sequences: A132666, A132667, A132668, A132669.
Other related sequences for different p: A016116(p=2), A133626(p=3), A084221(p=4), A133632(p=5).
Sequence in context: A005514 A069921 A053818 this_sequence A048010 A002571 A077916
Adjacent sequences: A133626 A133627 A133628 this_sequence A133630 A133631 A133632
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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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