A116483 -id:A116483 - cp's OEIS frontend

A116484 Expansion of (-1+3x)/(5x^2 + 1 - 2*x).

-1, 1, 7, 9, -17, -79, -73, 249, 863, 481, -3353, -9111, -1457, 42641, 92567, -28071, -518977, -897599, 799687, 6087369, 8176303, -14084239, -69049993, -67678791, 209892383, 758178721, 466895527, -2857102551, -8048682737, -1811852719

Offset: 0

Creighton Dement, Feb 17 2006

Binomial transform of signed powers of 2: (-1, 2, 4, -8, -16, 32, 64, -128, -256, 512, 1024). Inverse binomial transform of (-1, 0, 8, 32, 64, 0, -512, -2048, -4096, 0, 32768, 131072, 262144, 0, -2097152, -8388608). Compare with A116483.

Floretion Algebra Multiplication Program, FAMP Code: 2basekforseq[A*B] with A = - .5'i + .5'j - .5i' + .5j' + 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj' and B = - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' ; 1vesforseq = A000004

Harvey P. Dale, Table of n, a(n) for n = 0..1000
J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222.
J. Riordan, The distribution of crossings of chords joining pairs of 2n points on a circle, Math. Comp., 29 (1975), 215-222. [Annotated scanned copy]
Index entries for linear recurrences with constant coefficients, signature (2,-5).

Cf. A000079, A006495, A116483.

CoefficientList[Series[(-1+3x)/(5x^2+1-2x),{x,0,40}],x] (* or *) LinearRecurrence[{2,-5},{-1,1},40] (* Harvey P. Dale, Jun 24 2013 *)

a(n) = 3*A045873(n) - A045873(n+1). - R. J. Mathar, Apr 23 2009
E.g.f.: exp(x)*(sin(2*x) - cos(2*x)). - Arkadiusz Wesolowski, Aug 31 2012
a(0)=-1, a(1)=1, a(n) = 2*a(n-1) - 5*a(n-2). - Harvey P. Dale, Jun 24 2013
a(n) = (1/2)*((-1 - i)*(1 + 2*i)^n - (1 - i)*(1 - 2*i)^n), n >= 0, where i=sqrt(-1). - Taras Goy, Apr 20 2019

A138749 a(n) = 2a(n-1) - 5a(n-2), with a(1) = -1, a(2) = -7.

Original entry on oeis.org

-1, -7, -9, 17, 79, 73, -249, -863, -481, 3353, 9111, 1457, -42641, -92567, 28071, 518977, 897599, -799687, -6087369, -8176303, 14084239, 69049993, 67678791, -209892383, -758178721, -466895527, 2857102551, 8048682737, 1811852719, -36619708247

Offset: 1

Gary W. Adamson, Mar 28 2008

			a(5) = 79 = 2*a(4) - 5*a(3) = 2*17 - 5*(-9).
a(5) = 79 = left term in [1,-2, 2,1]^5.

Index entries for linear recurrences with constant coefficients, signature (2,-5).

Rest[CoefficientList[Series[-x*(1+5*x)/(1-2*x+5*x^2),{x,0,30}],x]] (* or *) LinearRecurrence[{2,-5},{-1,-7},30] (* James C. McMahon, Jun 21 2025 *)

a(n)={local(v=Vec((1+2*I*x)^n)); sum(k=1,#v, real(v[k])-imag(v[k]));} /* cf. A116483 */ /* Joerg Arndt, Jul 06 2011 */

a(n) = 2*a(n-1) - 5*a(n-2), n>3.
a(n) = left term in [1,-2; 2,1]^n * [1,1].
O.g.f.: -x*(1+5*x)/(1-2*x+5*x^2). a(n)=-A045873(n)-5*A045873(n-1). - R. J. Mathar, Apr 03 2008
a(n) = (1/2)*(1+i)*((1+2*i)^n-i*(1-2*i)^n), where i=sqrt(-1). - Bruno Berselli, Jul 06 2011

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A116484 Expansion of (-1+3x)/(5x^2 + 1 - 2*x).

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A138749 a(n) = 2a(n-1) - 5a(n-2), with a(1) = -1, a(2) = -7.

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cp's OEIS Frontend

A116484 Expansion of (-1+3*x)/(5*x^2 + 1 - 2*x).

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A138749 a(n) = 2*a(n-1) - 5*a(n-2), with a(1) = -1, a(2) = -7.

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A116484 Expansion of (-1+3x)/(5x^2 + 1 - 2*x).

A138749 a(n) = 2a(n-1) - 5a(n-2), with a(1) = -1, a(2) = -7.