A141516 - OEIS

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A141516

The main diagonal of the array of A141425 and its higher order differences.

1, 2, 1, -7, -23, -1, 7, -103, -251, -133, -149, -1387, -3143, -3001, -4913, -19663, -42611, -55693, -101549, -291667, -612863, -960001, -1831433, -4460023, -9185771, -15980053, -31162949, -69500347, -141392183, -261261001 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`The sequence A141425 and higher order differences in subsequent rows starts (see A141533):` `1, 2, 4, 5, 7, 8, 1, 2, 4, 5, 7, 8, 1, 2, 4,...` `1, 2, 1, 2, 1,-7, 1, 2, 1, 2, 1,-7, 1, 2, 1, 2,...` `1,-1, 1, -1, -8, 8, 1,-1, 1, -1, -8, 8, 1, -1,..` `-2, 2,-2, -7, 16,-7,-2, 2,-2, -7, 16,-7, -2,..` `4,-4,-5, 23,-23, 5, 4,-4,-5, 23,-23, 5, 4,..` `-8,-1,28,-46, 28,-1,-8,-1,28,-46, 28,-1,..` `Reading downwards the main diagonal of this array defines the sequence.`
	LINKS	`Index to sequences with linear recurrences with constant coefficients, signature (1,-1,3,6)`
	FORMULA	`a(n) = ( -3(-1)^n -2^n +3(-1)^(floor((n-1)/2))A108411(n) )/2, n>0 - R. J. Mathar, Mar 08 2011` `a(2n)+a(2n+1)= -A002023(n-1) = -3A081294(n), n>0 .` `a(4n)+a(4n+1)+a(4n+2)+a(4n+3) = -12016^(n-1), n>0.` `a(4n+2)+a(4n+3)+a(4n+4)+a(4n+5) = -30A001025(n).` `G.f. x(-2+x+6x^2+21x^3) / ( (2x-1)(1+x)(3*x^2+1) ). - R. J. Mathar, Mar 08 2011`
	MAPLE	`A108411 := proc(n) 3^floor(n/2) ; end proc:` `A141516 := proc(n) if n = 0 then 1; else (-3(-1)^n-2^n+3(-1)^(floor((n-1)/2))*A108411(n))/2 ; end if; end proc: # R. J. Mathar, Mar 08 2011`
	CROSSREFS	`Sequence in context: A012893 A013075 A009281 * A183272 A138346 A085073` `Adjacent sequences: A141513 A141514 A141515 * A141517 A141518 A141519`
	KEYWORD	`sign,easy`
	AUTHOR	`Paul Curtz (bpcrtz(AT)free.fr), Aug 11 2008`

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Last modified February 16 17:48 EST 2012. Contains 205939 sequences.