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A261711 Triangle read by rows: T(n,k) is the number of words over alphabet {0,1,2,3} having exactly k occurrences of the string 01, where n>=0 and k>=0. 1
1, 4, 15, 1, 56, 8, 209, 46, 1, 780, 232, 12, 2911, 1091, 93, 1, 10864, 4912, 592, 16, 40545, 21468, 3366, 156, 1, 151316, 91824, 17784, 1200, 20, 564719, 386373, 89238, 8010, 235, 1, 2107560, 1604984, 430992, 48624, 2120, 24, 7865521, 6598282, 2021103, 275724, 16255, 330, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

Ran Pan, Problem 5, Project P.

FORMULA

G.f.: 1/(1-4*x-(y-1)*x^2).

EXAMPLE

1

4

15 1

56 8

209 46 1

780 232 12

2911 1091 93 1

10864 4912 592 16

40545 21468 3366 156 1

151316 91824 17784 8010 20

MAPLE

b:= proc(n, t) option remember; expand(`if`(n=0, 1,

      add(b(n-1, i)*`if`(t=1 and i=2, x, 1), i=1..4)))

    end:

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

seq(T(n), n=0..12);  # Alois P. Heinz, Aug 29 2015

CROSSREFS

Column k=0 is A001353(n+1). The triangle is shifted from A207823.

Sequence in context: A097548 A218047 A127910 * A128235 A024547 A143899

Adjacent sequences:  A261708 A261709 A261710 * A261712 A261713 A261714

KEYWORD

easy,nonn,tabf

AUTHOR

Ran Pan, Aug 29 2015

STATUS

approved

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Last modified September 26 06:54 EDT 2017. Contains 292502 sequences.