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A271532 a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1). 0
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..38.

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 xrange(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

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

Sequence in context: A203965 A203958 A005903 * A264480 A247155 A239728

Adjacent sequences:  A271529 A271530 A271531 * A271533 A271534 A271535

KEYWORD

sign,easy

AUTHOR

Ilya Gutkovskiy, Apr 09 2016

STATUS

approved

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Last modified October 16 20:34 EDT 2018. Contains 316275 sequences. (Running on oeis4.)