A271532 a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1).
1, -32, 123, -304, 605, -1056, 1687, -2528, 3609, -4960, 6611, -8592, 10933, -13664, 16815, -20416, 24497, -29088, 34219, -39920, 46221, -53152, 60743, -69024, 78025, -87776, 98307, -109648, 121829, -134880, 148831, -163712, 179553, -196384, 214235, -233136, 253117, -274208, 296439
Offset: 0
Links
- OEIS Wiki, Centered Platonic numbers
- Eric Weisstein's World of Mathematics, Platonic Solid
- Index entries for linear recurrences with constant coefficients, signature (-4,-6,-4,-1)
Programs
-
Mathematica
Table[(-1)^n (n + 1) (5 n^2 + 10 n + 1), {n, 0, 38}] LinearRecurrence[{-4, -6, -4, -1}, {1, -32, 123, -304}, 39] -
PARI
a(n)=(-1)^n*(n+1)*(5*n^2+10*n+1) \\ Charles R Greathouse IV, Jul 26 2016
-
Python
for n in range(0,10**3):print((-1)**n*(n+1)*(5*n**2+10*n+1)) # Soumil Mandal, Apr 10 2016
Formula
G.f.: (1 - 28*x + x^2)/(1 + x)^4.
E.g.f.: exp(-x)*(1 - 31*x + 30*x^2 - 5*x^3).
a(n) = -4*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4).
Comments