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 A110513 Expansion of (1 + x)/(1 + 2x + x^3). 4
 1, -1, 2, -5, 11, -24, 53, -117, 258, -569, 1255, -2768, 6105, -13465, 29698, -65501, 144467, -318632, 702765, -1549997, 3418626, -7540017, 16630031, -36678688, 80897393, -178424817, 393528322, -867954037, 1914332891, -4222194104, 9312342245, -20539017381, 45300228866, -99912799977 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Diagonal sums of A110511. LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-2,0,-1). FORMULA a(n) = Sum_{k=0..floor(n/2)} Sum_{j=0..(n-k)} (-1)^(n-k-j)*C(n-k, j)*(-2)^(j-k)*C(k, j-k). a(0)=1, a(1)=-1, a(2)=2, a(n) = -2*a(n-1) - a(n-3). - Harvey P. Dale, Jun 27 2012 MATHEMATICA CoefficientList[Series[(1+x)/(1+2x+x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[ {-2, 0, -1}, {1, -1, 2}, 40] (* Harvey P. Dale, Jun 27 2012 *) PROG (PARI) x='x+O('x^50); Vec((1+x)/(1+2x+x^3)) \\ G. C. Greubel, Aug 29 2017 CROSSREFS A minor variation of A052980. Sequence in context: A077864 A052980 A190512 * A018115 A242551 A018007 Adjacent sequences: A110510 A110511 A110512 * A110514 A110515 A110516 KEYWORD easy,sign AUTHOR Paul Barry, Jul 24 2005 STATUS approved

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Last modified April 15 03:58 EDT 2024. Contains 371667 sequences. (Running on oeis4.)