A181657 -id:A181657 - cp's OEIS frontend

A181658 Row sums of A181657.

1, 2, 3, 7, 8, 19, 20, 48, 49, 118, 119, 287, 288, 695, 696, 1680, 1681, 4058, 4059, 9799, 9800, 23659, 23660, 57120, 57121, 137902, 137903, 332927, 332928, 803759, 803760, 1940448, 1940449, 4684658, 4684659, 11309767, 11309768, 27304195, 27304196

Offset: 0

Paul Barry, Nov 03 2010

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-1,0,-1)

Cf. A048739 (bisection).

CoefficientList[Series[(1+2x+x^3)/(1-3x^2+x^4+x^6),{x,0,40}],x] (* or *) LinearRecurrence[{0,3,0,-1,0,-1},{1,2,3,7,8,19},40] (* Harvey P. Dale, Mar 29 2022 *)

G.f.: (1+2x+x^3)/(1-3x^2+x^4+x^6)=(1+2x+x^3)/((1-x^2)(1-2x^2-x^4)).

A181656 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x^2) if k mod 2 = 0, x^k(1+x) otherwise.

Original entry on oeis.org

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

Offset: 0

Paul Barry, Nov 03 2010

A181657 is an eigentriangle for this triangle.

			Triangle begins
  1;
  0, 1;
  1, 1, 1;
  0, 0, 0, 1;
  0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 1, 1, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
  0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1;
Production matrix begins
   0,  1;
   1,  1,  1;
  -1, -2, -1,  1;
   0,  0,  1,  1,  1;
   1,  2,  0, -2, -1,  1;
   0,  0,  0,  0,  1,  1,  1;
  -1, -2,  0,  2,  0, -2, -1,  1;
   0,  0,  0,  0,  0,  0,  1,  1,  1;
   1,  2,  0, -2,  0,  2,  0, -2, -1,  1;
   0,  0,  0,  0,  0,  0,  0,  0,  1,  1,  1;

cp's OEIS Frontend

A181658 Row sums of A181657.

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A181656 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x^2) if k mod 2 = 0, x^k(1+x) otherwise.

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cp's OEIS Frontend

A181658 Row sums of A181657.

Views

Author

Keywords

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Programs

Mathematica

Formula

A181656 Generalized (conditional) Riordan array with k-th column generated by x^k*(1+x^2) if k mod 2 = 0, x^k*(1+x) otherwise.

Views

Author

Keywords

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Examples

A181656 Generalized (conditional) Riordan array with k-th column generated by x^k(1+x^2) if k mod 2 = 0, x^k(1+x) otherwise.