OFFSET
0,3
LINKS
Daniel Mondot, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
Eric Weisstein's World of Mathematics, Square Number
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
O.g.f.: x*(1 + 189*x + 1250*x^2 + 1250*x^3 + 189*x^4 + x^5)/(1 - x)^7.
E.g.f.: x*(1 + 97*x + 336*x^2 + 256*x^3 + 60*x^4 + 4*x^5)*exp(x).
a(n) = a(-n).
a(n) = n^2*(2*n^2 - 1)^2.
Sum_{n>=1} 1/a(n) = (2*Pi^2+9*sqrt(2)*Pi*cot(Pi/sqrt(2))+3*Pi^2*csc(Pi/sqrt(2))^2-24)/12 = 1.0055779712856...
EXAMPLE
a(2) = 196 because 196 = 14^2 is a perfect square and 196 = 7^2*(7 + 1)/2 is the 7th pentagonal pyramidal number.
MATHEMATICA
Table[n^2 (2 n^2 - 1)^2, {n, 0, 30}]
PROG
(Magma) [n^2*(2*n^2-1)^2: n in [0..30]]; // Vincenzo Librandi, Nov 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Oct 31 2016
STATUS
approved