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a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1).
0

%I #23 Dec 07 2019 12:18:28

%S 1,-32,123,-304,605,-1056,1687,-2528,3609,-4960,6611,-8592,10933,

%T -13664,16815,-20416,24497,-29088,34219,-39920,46221,-53152,60743,

%U -69024,78025,-87776,98307,-109648,121829,-134880,148831,-163712,179553,-196384,214235,-233136,253117,-274208,296439

%N a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1).

%C Alternating sum of centered dodecahedral numbers (A005904).

%C Without signs and up to offset, this is row 5 of the array A284873. - _Andrey Zabolotskiy_, Oct 10 2017

%H OEIS Wiki, <a href="https://oeis.org/wiki/Centered_Platonic_numbers">Centered Platonic numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PlatonicSolid.html">Platonic Solid</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-6,-4,-1)

%F G.f.: (1 - 28*x + x^2)/(1 + x)^4.

%F E.g.f.: exp(-x)*(1 - 31*x + 30*x^2 - 5*x^3).

%F a(n) = -4*a(n-1) - 6*a(n-2) - 4*a(n-3) - a(n-4).

%t Table[(-1)^n (n + 1) (5 n^2 + 10 n + 1), {n, 0, 38}]

%t LinearRecurrence[{-4, -6, -4, -1}, {1, -32, 123, -304}, 39]

%o (Python) for n in range(0,10**3):print((-1)**n*(n+1)*(5*n**2+10*n+1)) # _Soumil Mandal_, Apr 10 2016

%o (PARI) a(n)=(-1)^n*(n+1)*(5*n^2+10*n+1) \\ _Charles R Greathouse IV_, Jul 26 2016

%Y Cf. A000578, A004466, A005904, A006527, A005900, A006566.

%K sign,easy

%O 0,2

%A _Ilya Gutkovskiy_, Apr 09 2016