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A190705

a(n) = 6*n^2*(2*n + 1).

0, 18, 120, 378, 864, 1650, 2808, 4410, 6528, 9234, 12600, 16698, 21600, 27378, 34104, 41850, 50688, 60690, 71928, 84474, 98400, 113778, 130680, 149178, 169344, 191250, 214968, 240570, 268128, 297714, 329400 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`Number of partitions of 12*n + 1 into 4 parts.`
	LINKS	`Vincenzo Librandi, Table of n, a(n) for n = 0..1000` `Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).`
	FORMULA	`a(n) = 6 * A099721(n).` `a(n) = 4a(n-1) - 6a(n-2) + 4*a(n-3) - a(n-4); a(0)=0, a(1)=18, a(2)=120, a(3)=378. - Harvey P. Dale, Mar 20 2016`
	EXAMPLE	`a(1)=18: there are 18 partitions of 12*1+1=13 into 4 parts:` `[1,1,1,10], [1,1,2,9], [1,1,3,8], [1,1,4,7], [1,1,5,6],` `[1,2,2,8], [1,2,3,7], [1,2,4,6], [1,2,5,5], [1,3,3,6],` `[1,3,4,5], [1,4,4,4], [2,2,2,7], [2,2,3,6], [2,2,4,5],` `[2,3,3,5], [2,3,4,4], [3,3,3,4].`
	MATHEMATICA	`Table[6n^2(2n + 1), {n, 0, 30}]` `LinearRecurrence[{4, -6, 4, -1}, {0, 18, 120, 378}, 40] (* Harvey P. Dale, Mar 20 2016 *)`
	PROG	`(Magma) [6n^2(2n+1): n in [0..40]]; // Vincenzo Librandi, Jun 14 2011` `(PARI) a(n)=6n^2(2n+1) \\ Charles R Greathouse IV, Aug 05 2013`
	CROSSREFS	`Sequence in context: A293878 A044350 A044731 * A108648 A264360 A223046` `Adjacent sequences: A190702 A190703 A190704 * A190706 A190707 A190708`
	KEYWORD	`nonn,easy`
	AUTHOR	`Adi Dani, Jun 14 2011`
	STATUS	`approved`

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Last modified August 21 12:48 EDT 2024. Contains 375353 sequences. (Running on oeis4.)