OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (1, 0, 3, -3, 0, -3, 3, 0, 1, -1).
FORMULA
From Ant King, Oct 24 2012: (Start)
a(n) = a(n-1) +3*a(n-3) -3*a(n-4) -3*a(n-6) +3*a(n-7) +a(n-9) -a(n-10).
a(n) = 3*a(n-3) -3*a(n-6) +a(n-9) +192.
Sum_{n>=0} 1/a(n) = log(2)/2 + Pi/4 + 5*Pi^2/24 - 2 - C = 0.27217..., where C is Catalan's constant (A006752).
G.f.: 2*x*(3+6*x+11*x^2+34*x^3+17*x^4+13*x^5+11*x^6+x^7) / ((1-x)^4*(1+x +x^2)^3). (End)
MATHEMATICA
LinearRecurrence[{1, 0, 3, -3, 0, -3, 3, 0, 1, -1}, {0, 6, 18, 40, 126, 196, 288, 550, 726, 936}, 40] (* Ant King, Oct 19 2012 *)
PROG
(PARI) x='x+O('x^30); concat([0], Vec(2*x*(3+6*x+11*x^2+34*x^3 +17*x^4 +13*x^5+11*x^6+x^7)/((1-x)^4*(1+x +x^2)^3))) \\ G. C. Greubel, Aug 24 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!(2*x*(3+6*x+11*x^2+34*x^3+17*x^4+13*x^5+11*x^6+x^7)/((1-x)^4*(1+x +x^2)^3))); // G. C. Greubel, Aug 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, Jul 14 1999
STATUS
approved