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A008354 (5*n^2 + 1) * n^2 / 6. 3
0, 1, 14, 69, 216, 525, 1086, 2009, 3424, 5481, 8350, 12221, 17304, 23829, 32046, 42225, 54656, 69649, 87534, 108661, 133400, 162141, 195294, 233289, 276576, 325625, 380926, 442989, 512344, 589541 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Omitting the leading 0, these are the partial sums of the centered icosahedral (or cuboctahedral) numbers (A005902). - Jonathan Vos Post, Mar 14 2006

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

O.g.f.: x(1+x)(x^2+8x+1)/(1-x)^5. a(n) = n*A004068(n). - R. J. Mathar, Aug 10 2008

a(0)=0, a(1)=1, a(2)=14, a(3)=69, a(4)=216, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Feb 12 2015

MAPLE

5*n^4/6 + n^2/6;

MATHEMATICA

Table[(n^2 (5n^2+1))/6, {n, 0, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 14, 69, 216}, 30] (* Harvey P. Dale, Feb 12 2015 *)

CROSSREFS

Cf. A005901, A005902, A008354.

Sequence in context: A238822 A244943 A249708 * A051879 A236157 A002423

Adjacent sequences:  A008351 A008352 A008353 * A008355 A008356 A008357

KEYWORD

nonn

AUTHOR

N. J. A. Sloane and J. H. Conway

EXTENSIONS

Definition corrected by R. J. Mathar, Aug 10 2008

STATUS

approved

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Last modified August 22 20:43 EDT 2017. Contains 290951 sequences.