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 A133629 a(1)=1, a(n) = a(n-1) + (p-1)*p^(n/2-1) if n is even, otherwise a(n) = a(n-1) + p^((n-1)/2), where p=5. 6
 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, 38146972655, 68664550780 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Partial sums of A133632. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,5,-5). FORMULA a(n) = Sum_{k=1..n} A133632(k). The following formulas are given for a general natural parameter p > 1 (p=5 for this sequence). G.f.: x(1+(p-1)x)/((1-px^2)(1-x)). a(n) = (p/(p-1))*(p^(n/2)-1) if n is even, otherwise 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. From Colin Barker, Nov 25 2016: (Start) a(n) = 5*(5^(n/2) - 1)/4 for n even. a(n) = (9*5^(n/2-1/2) - 5)/4 for n odd. a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) for n > 3. G.f.: x*(1 + 4*x) / ((1 - x) * (1 - 5*x^2)). (End) MAPLE 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, Mar 17 2008 PROG (PARI) Vec(x*(1 + 4*x) / ((1 - x) * (1 - 5*x^2)) + O(x^40)) \\ Colin Barker, Nov 25 2016 CROSSREFS Sequences with similar recurrence rules: A027383 (p=2), A087503 (p=3), A133628 (p=4). Related sequences: A132666, A132667, A132668, A132669. Other related sequences for different p: A016116 (p=2), A038754 (p=3), A084221 (p=4), A133632 (p=5). Sequence in context: A069921 A053818 A294286 * A156302 A156234 A048010 Adjacent sequences:  A133626 A133627 A133628 * A133630 A133631 A133632 KEYWORD nonn,easy AUTHOR Hieronymus Fischer, Sep 19 2007 STATUS approved

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Last modified July 26 22:49 EDT 2021. Contains 346300 sequences. (Running on oeis4.)