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A277678 Number T(n,k) of binary words of length n containing exactly k (possibly overlapping) occurrences of the subword 11011; triangle T(n,k), n>=0, k=0..max(0,floor((n-2)/3)), read by rows. 3
1, 2, 4, 8, 16, 31, 1, 60, 4, 116, 12, 225, 30, 1, 437, 70, 5, 849, 158, 17, 1649, 351, 47, 1, 3202, 770, 118, 6, 6217, 1669, 283, 23, 12071, 3578, 664, 70, 1, 23438, 7599, 1535, 189, 7, 45510, 16016, 3500, 480, 30, 88368, 33545, 7876, 1182, 100, 1, 171586 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Rows n = 0..350, flattened

FORMULA

G.f. of column k=0: -(x^4+x^3+1)/(x^5+x^4-x^3+2*x-1); g.f. of column k>0: x^5*(x^3*(x^2+x-1))^(k-1)/(x^5+x^4-x^3+2*x-1)^(k+1).

Sum_{k>=0} k * T(n,k) = A001787(n-4) for n>3.

EXAMPLE

Triangle T(n,k) begins:

:     1;

:     2;

:     4;

:     8;

:    16;

:    31,   1;

:    60,   4;

:   116,  12;

:   225,  30,   1;

:   437,  70,   5;

:   849, 158,  17;

:  1649, 351,  47, 1;

:  3202, 770, 118, 6;

MAPLE

b:= proc(n, t) option remember; expand(

      `if`(n=0, 1,     b(n-1, [1, 1, 4, 1, 1][t])+

      `if`(t=5, x, 1)* b(n-1, [2, 3, 3, 5, 3][t])))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..degree(p)))(b(n, 1)):

seq(T(n), n=0..20);

# second Maple program:

gf:= k-> `if`(k=0, -(x^4+x^3+1), x^5*(x^3*(x^2+x-1))^(k-1))

                   /(x^5+x^4-x^3+2*x-1)^(k+1):

T:= (n, k)-> coeff(series(gf(k), x, n+1), x, n):

seq(seq(T(n, k), k=0..max(0, floor((n-2)/3))), n=0..20);

CROSSREFS

Column k=0 gives A210021.

Row sums give A000079.

Row sums except column k=0 give A276785.

Cf. A001787, A002264.

Sequence in context: A244825 A220843 A277751 * A018763 A054517 A054016

Adjacent sequences:  A277675 A277676 A277677 * A277679 A277680 A277681

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Oct 26 2016

STATUS

approved

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Last modified May 31 19:40 EDT 2020. Contains 334748 sequences. (Running on oeis4.)