A263418 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
1, 6, 21, 51, 106, 201, 361, 626, 1061, 1771, 2926, 4801, 7841, 12766, 20741, 33651, 54546, 88361, 143081, 231626, 374901, 606731, 981846, 1588801, 2570881, 4159926, 6731061, 10891251, 17622586, 28514121, 46137001, 74651426, 120788741, 195440491, 316229566
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Kival Ngaokrajang, Illustration of initial terms
- Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).
Programs
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PARI
{a=1; print1(a, ", "); for(n=1,100, b=fibonacci(n+3)-2; a=a+5*b; print1 (a, ", "))} -
PARI
Vec(-(x^3+5*x^2+3*x+1)/((x-1)^2*(x^2+x-1)) + O(x^50)) \\ Colin Barker, Oct 18 2015
Formula
a(0) = 1, for n > 0, a(n) = a(n-1) + 5*(fibonacci(n+3)-2) or a(n) = a(n-1) + 5*A001911(n).
From Colin Barker, Oct 18 2015: (Start)
a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4) for n>3.
G.f.: -(x^3+5*x^2+3*x+1) / ((x-1)^2*(x^2+x-1)).
(End)
a(n) = -14 + 2^(-1-n)*((25-11*sqrt(5))*(1-sqrt(5))^n + (1+sqrt(5))^n*(25+11*sqrt(5))) - 10*(1+n). - Colin Barker, Mar 12 2017
Comments