A072827 - OEIS

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A072827

Number of permutations satisfying i-2<=p(i)<=i+3, i=1..n.

1, 2, 6, 18, 46, 115, 301, 792, 2068, 5380, 14020, 36581, 95413, 248786, 648714, 1691686, 4411530, 11503991, 29998953, 78228640, 203998184, 531969064, 1387222648, 3617479225, 9433351129, 24599481138, 64148406350, 167280683834 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`1,2`
	LINKS	`R. H. Hardin, Table of n, a(n) for n = 1..400` `Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135.` `Index entries for linear recurrences with constant coefficients, signature (1,2,3,5,6,-1,-1,0,-1,-1).`
	FORMULA	`Recurrence: a(n) = a(n-1)+2a(n-2)+3a(n-3)+5a(n-4)+6a(n-5)-a(n-6)-a(n-7)-a(n-9)-a(n-10).` `G.f.: (1-x^5-x^3-x^2)/(x^10+x^9+x^7+x^6-6x^5-5x^4-3x^3-2x^2-x+1). [Corrected by Georg Fischer, May 15 2019]`
	MATHEMATICA	`LinearRecurrence[{1, 2, 3, 5, 6, -1, -1, 0, -1, -1}, {1, 2, 6, 18, 46, 115, 301, 792, 2068, 5380}, 30] (* Harvey P. Dale, Aug 15 2014 *)`
	PROG	`(PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; -1, -1, 0, -1, -1, 6, 5, 3, 2, 1]^(n-1)*[1; 2; 6; 18; 46; 115; 301; 792; 2068; 5380])[1, 1] \\ Charles R Greathouse IV, Jul 28 2015`
	CROSSREFS	`Cf. A002524, A002525, A002526, A002527, A002528, A002529, A072850, A072851, A072852, A072853, A072854, A072855, A072856, A079955-A080014.` `Sequence in context: A054136 A232600 A140960 * A248169 A002529 A217526` `Adjacent sequences: A072824 A072825 A072826 * A072828 A072829 A072830`
	KEYWORD	`nonn,easy`
	AUTHOR	`Vladimir Baltic, Jul 21 2002`
	STATUS	`approved`

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Last modified September 30 22:28 EDT 2022. Contains 357107 sequences. (Running on oeis4.)