OFFSET
0,2
COMMENTS
Partial sums of centered dodecahedral numbers (A005904).
LINKS
OEIS Wiki, Centered Platonic numbers
Eric Weisstein's World of Mathematics, Platonic Solid
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)
FORMULA
G.f.: (1 + 29*x + 29*x^2 + x^3)/(1 - x)^5.
E.g.f.: exp(x)*(2 + 66*x + 122*x^2 + 50*x^3 + 5*x^4)/2.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
Sum_{n>=0} 1/a(n) = (5 - Pi^2 - sqrt(15)*Pi*cot(sqrt(3/5)*Pi))/9 = 1.0377796966... . - Vaclav Kotesovec, Apr 10 2016
MAPLE
A269237:=n->(n + 1)^2*(5*n^2 + 10*n + 2)/2: seq(A269237(n), n=0..50); # Wesley Ivan Hurt, Oct 15 2017
MATHEMATICA
Table[(n + 1)^2 ((5 n^2 + 10 n + 2)/2), {n, 0, 35}]
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 34, 189, 616, 1525}, 36]
PROG
(PARI) x='x+O('x^99); Vec((1+29*x+29*x^2+x^3)/(1-x)^5) \\ Altug Alkan, Apr 10 2016
(Magma) [(n + 1)^2*(5*n^2 + 10*n + 2)/2 : n in [0..50]]; // Wesley Ivan Hurt, Oct 15 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Apr 09 2016
STATUS
approved