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
KEYWORD
nonn,easy
AUTHOR
Hieronymus Fischer, Sep 19 2007
STATUS
approved