A181654 -id:A181654 - cp's OEIS frontend

A181655 Expansion of (1+2x-x^3+x^4)/(1-4x^2+3x^4).

1, 2, 4, 7, 14, 22, 44, 67, 134, 202, 404, 607, 1214, 1822, 3644, 5467, 10934, 16402, 32804, 49207, 98414, 147622, 295244, 442867, 885734, 1328602, 2657204, 3985807, 7971614, 11957422, 23914844, 35872267, 71744534, 107616802, 215233604

Offset: 0

Paul Barry, Nov 03 2010

Row sums of A181654.

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-3).

Cf. A060816, A198643 (bisections).

CoefficientList[Series[(1+2x-x^3+x^4)/(1-4x^2+3x^4),{x,0,40}],x] (* or *) Join[{1},LinearRecurrence[{0,4,0,-3},{2,4,7,14},40]] (* Harvey P. Dale, Jan 11 2012 *)

A181655(n)=if(bitand(n,1), 3^(n\2)*5\2, n, 3^(n\2-1)*5-1, 1) \\ M. F. Hasler, Apr 06 2019

G.f.: (1+2*x-x^3+x^4)/((1-x^2)*(1-3*x^2)).
a(n) = 5*A038754(n+1)/6 - A040001(n)/2. - R. J. Mathar, May 14 2016
a(2n-1) = A060816(n-1), a(2n) = A198643(n-1); n >= 1. a(n+1) = 2*a(n) if n is odd. - M. F. Hasler, Apr 06 2019

A181653 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x) if k mod 2 = 0, x^k(1+x+x^2) otherwise.

Original entry on oeis.org

1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1

Offset: 0

Paul Barry, Nov 03 2010

Row sums are A174296. A181654 is an eigentriangle.

			Triangle begins
  1;
  1, 1;
  0, 1, 1;
  0, 1, 1, 1;
  0, 0, 0, 1, 1;
  0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 1, 1;
  0, 0, 0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 0, 0, 1, 1;
  0, 0, 0, 0, 0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1;
Production matrix begins
   1,  1;
  -1,  0,  1;
   1,  1,  0,  1;
   0, -1, -1,  0,  1;
   0,  1,  1,  1,  0,  1;
   0,  0,  0, -1, -1,  0,  1;
   0,  0,  0,  1,  1,  1,  0,  1;
   0,  0,  0,  0,  0, -1, -1,  0,  1;
   0,  0,  0,  0,  0,  1,  1,  1,  0,  1;
   0,  0,  0,  0,  0,  0,  0, -1, -1,  0,  1;

cp's OEIS Frontend

A181655 Expansion of (1+2x-x^3+x^4)/(1-4x^2+3x^4).

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A181653 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x) if k mod 2 = 0, x^k(1+x+x^2) otherwise.

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cp's OEIS Frontend

A181655 Expansion of (1+2x-x^3+x^4)/(1-4x^2+3x^4).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A181653 Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x) if k mod 2 = 0, x^k*(1+x+x^2) otherwise.

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A181653 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x) if k mod 2 = 0, x^k(1+x+x^2) otherwise.