OFFSET
0,2
COMMENTS
Alternating sum of centered dodecahedral numbers (A005904).
Without signs and up to offset, this is row 5 of the array A284873. - Andrey Zabolotskiy, Oct 10 2017
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)
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).
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]
PROG
(Python) for n in range(0, 10**3):print((-1)**n*(n+1)*(5*n**2+10*n+1)) # Soumil Mandal, Apr 10 2016
(PARI) a(n)=(-1)^n*(n+1)*(5*n^2+10*n+1) \\ Charles R Greathouse IV, Jul 26 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Ilya Gutkovskiy, Apr 09 2016
STATUS
approved