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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.)