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 A138112 a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4), a(0)=a(1)=a(2)=0, a(3)=1, a(4)=3. 5
 0, 0, 0, 1, 3, 5, 5, 0, -13, -34, -55, -55, 0, 144, 377, 610, 610, 0, -1597, -4181, -6765, -6765, 0, 17711, 46368, 75025, 75025, 0, -196418, -514229, -832040, -832040, 0, 2178309, 5702887, 9227465, 9227465, 0, -24157817, -63245986, -102334155, -102334155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Obeys also the recurrence a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5), so the sequence is identical to its fifth differences (cf. A135356). a(n) = A138110(0,n): if A138110 is interpreted as an array with five rows, this is the top row. The first differences are represented by A100334(n-1). The 2nd differences are represented by A103311(n). The 3rd differences are essentially represented by -A138003(n-2). The 4th differences are represented by -A105371(n). A102312 contains the absolute values of the terms which occur in pairs, for example a(5)=a(6)=5=A102312(1), a(10)=a(11)= -55 = -A102312(2). Inverse BINOMIAL transform yields two zeros followed by A105384. - R. J. Mathar, Jul 04 2008 LINKS Index entries for linear recurrences with constant coefficients, signature (3, -4, 2, -1). FORMULA O.g.f.: x^3/(1-3x+4x^2-2x^3+x^4). - R. J. Mathar, Jul 04 2008 MATHEMATICA CoefficientList[Series[x^3/(1-3x+4x^2-2x^3+x^4), {x, 0, 45}], x] (* or *) LinearRecurrence[{3, -4, 2, -1}, {0, 0, 0, 1}, 45] (* Harvey P. Dale, Jun 22 2011 *) CROSSREFS Cf. A138003, A103311, A105371. Sequence in context: A284867 A152416 A200334 * A106233 A198492 A077860 Adjacent sequences:  A138109 A138110 A138111 * A138113 A138114 A138115 KEYWORD sign AUTHOR Paul Curtz, May 04 2008 EXTENSIONS Edited and extended by R. J. Mathar, Jul 04 2008 STATUS approved

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Last modified August 21 18:38 EDT 2019. Contains 326168 sequences. (Running on oeis4.)