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A062026 a(n) = n(n+1)(n^2 -3n +6)/4 3
0, 2, 6, 18, 50, 120, 252, 476, 828, 1350, 2090, 3102, 4446, 6188, 8400, 11160, 14552, 18666, 23598, 29450, 36330, 44352, 53636, 64308, 76500, 90350, 106002, 123606, 143318, 165300, 189720, 216752, 246576, 279378, 315350, 354690, 397602, 444296 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = 1*2*3 + 2*3*4 + 3*4*5 +. . .+ (n-2)*(n-1)*n +(n-1)*n*1+ n*1*2, the sum of the cyclic product of terms taken three at a time, final term being n*1*2=2n.

LINKS

Harry J. Smith, Table of n, a(n) for n=0,...,1000

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

FORMULA

a(0)=0, a(1)=2, a(2)=6, a(3)=18, a(4)=50, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Apr 22 2015

EXAMPLE

a(4) = 1*2*3 + 2*3*4 + 3*4*1 + 4*1*2 = 50.

MATHEMATICA

Table[n(n+1)(n^2-3n+6)/4, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 2, 6, 18, 50}, 40] (* Harvey P. Dale, Apr 22 2015 *)

PROG

(PARI) { for (n=0, 1000, write("b062026.txt", n, " ", n*(n + 1)*(n^2 - 3*n + 6)/4) ) } \\ Harry J. Smith, Jul 29 2009

CROSSREFS

Equals 2 * A004255.

Sequence in context: A256828 A197055 A258625 * A048495 A089380 A271897

Adjacent sequences:  A062023 A062024 A062025 * A062027 A062028 A062029

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Jun 02 2001

EXTENSIONS

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001

STATUS

approved

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Last modified August 10 07:37 EDT 2020. Contains 336368 sequences. (Running on oeis4.)